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Page 11 of Mathematical Reviews Vol. 38, Issue 6 [page]

<span title="">1969</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Berkeley), pp. 190-205, North-Holland, Amster- dam, 1965; MR 33 #7257], the author introduces the new notions of invariant implicit definability and semi- invariant implicit definability intended to generalize  ...  Makkai (Budapest) 5596 Kunen, Kenneth 5597 Implicit definability and infinitary J. Symbolic Logic 38 (1968), 446-451. Following suggestions of R. Fraissé [Infinitistic methods (Proc. Sympos.  ... 
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Page 571 of Mathematical Reviews Vol. 38, Issue 4 [page]

<span title="">1969</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Barwise, Implicit definability and com- pactness in infinitary languages; C. C. Chang, Some re- marks on the model theory of infinitary languages; E.  ...  Kreisel, Choice of infinitary languages by means of definability criteria; generalized recursion theory; D. W. Kueker, Definability, automorphisms, and infinitary languages ; J.  ... 
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Page 6231 of Mathematical Reviews Vol. , Issue 96j [page]

<span title="">1996</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
In the paper connections between infinitary logic and some well-known restricted query languages (like fixpoint and while) are also examined.  ...  Summary: “In this paper we define the fuzzy Datalog programs as sets of Horn-formulae with degrees and give their meaning by defining a deterministic and nondeterministic semantics.  ... 
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Implicit definability of truth constants in Łukasiewicz logic [article]

Zuzana Haniková
<span title="2018-02-23">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In the framework of propositional Łukasiewicz logic, a suitable notion of implicit definability, tailored to the intended real-valued semantics and referring to the elements of its domain, is introduced  ...  Moreover, while irrational elements of the standard semantics are not implicitly definable by finitary means, a parallel development is possible for them in the infinitary Łukasiewicz logic.  ...  The author was supported by CE-ITI and GAČR under the grant number GBP202/12/G061, and by the long-term strategic development financing of the Institute of Computer Science RVO:67985807.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1802.08588v1">arXiv:1802.08588v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/snscv5neinbibmrrtch4h5a7rm">fatcat:snscv5neinbibmrrtch4h5a7rm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200901105716/https://arxiv.org/pdf/1802.08588v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0d/ee/0dee251aba2fb35238c3489afe16151593950917.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1802.08588v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Page 7536 of Mathematical Reviews Vol. , Issue 98M [page]

<span title="">1998</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The paper is mainly concerned with translating between Ga- lois cohomological language and the language of definable sets  ...  fixed point logic PFP, infinitary logic Y@., with a finite number of variables, and the closures of these logics under implicit definition.  ... 
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Infinitary propositional relevant languages with absurdity [article]

Guillermo Badia
<span title="2018-09-21">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
definability property.  ...  An "interpolation theorem" (of a particular sort introduced by Barwise and van Benthem) for the infinitary quantificational boolean logic L_∞ω holds.  ...  We are indebted to Zach Weber and Patrick Girard for their constant encouragement.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1809.08153v1">arXiv:1809.08153v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2qbrfh7i5zhdfjbr4viroz5zta">fatcat:2qbrfh7i5zhdfjbr4viroz5zta</a> </span>
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The exact strength of the class forcing theorem [article]

Victoria Gitman, Joel David Hamkins, Peter Holy, Philipp Schlicht, Kameryn Williams
<span title="2017-07-12">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
It is also equivalent to the existence of truth predicates for the infinitary languages L_Ord,ω(∈,A), allowing any class parameter A; to the existence of truth predicates for the language L_Ord,Ord(∈,A  ...  Our results situate the class forcing theorem in the rich hierarchy of theories between GBC and Kelley-Morse set theory KM.  ...  ; • the quantifier-free infinitary forcing language L Ord,0 (∈, V P ,Ġ); • the partial infinitary language L Ord,ω (∈,Â); • the full infinitary language L Ord,Ord (∈,Â). • the full infinitary forcing language  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1707.03700v1">arXiv:1707.03700v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/c37nu4ig7rfgdejri3vr7pdmo4">fatcat:c37nu4ig7rfgdejri3vr7pdmo4</a> </span>
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The Implicit Commitment of Arithmetical Theories and Its Semantic Core

Carlo Nicolai, Mario Piazza
<span title="2018-03-06">2018</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yehckvsrj5bznhjzgx5jrmywoq" style="color: black;">Erkenntnis: An International Journal of Scientific Philosophy</a> </i> &nbsp;
Traditionally, this thesis has been understood as entailing that, in accepting S, we are bound to accept reflection principles for S and therefore claims in the language of S that are not derivable in  ...  and Peano Arithmetic, Nelson's ultrafinitism and sub-exponential arithmetical systems.  ...  Acknowledgements We would like to thank Martin Fischer, Leon Horsten, and Graham Leigh for their comments to a previous version of the manuscript.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10670-018-9987-6">doi:10.1007/s10670-018-9987-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qx3ywat22jat5mjdvfrmmhquyi">fatcat:qx3ywat22jat5mjdvfrmmhquyi</a> </span>
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Functional interpretation and inductive definitions [article]

Jeremy Avigad, Henry Towsner
<span title="2009-02-17">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Extending Gödel's Dialectica interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined  ...  The interpretation of the logical axioms and rules are easily validated in the infinitary propositional calculus augmented with the cut rule, and the interpretation of the defining axioms for I α are trivially  ...  A similar setup is implicit in the interpretation of ID 1 due to Buchholz [7] , where a forcing interpretation is used in conjunction with an infinitary calculus akin to the one we have used here.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0802.1938v4">arXiv:0802.1938v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yxwafhc5rze7zcijmmxaidtbx4">fatcat:yxwafhc5rze7zcijmmxaidtbx4</a> </span>
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Editorial

M. Nivat
<span title="">1991</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
(including automata on infinite words and infinitary languages), the whole field of geometrical (graphic) applications and the whole field of measurement of system performance using statisticai methods  ...  Certainly it will include the whole field of abstract complexity (i.e., all the results about the hierarchies that can be defined using Turing machines), the whole field of automata and language theory  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(51)90001-1">doi:10.1016/0304-3975(51)90001-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/waalfug5ezg7flsotoqtbtmybi">fatcat:waalfug5ezg7flsotoqtbtmybi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190417111837/https://core.ac.uk/download/pdf/82487083.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e2/19/e2193971ae585427baf13f1f80c7519509f8216d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(51)90001-1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Page 891 of Mathematical Reviews Vol. , Issue 84c [page]

<span title="">1984</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
theory KP) in infinitary languages.  ...  Mints (Leningrad) Bergstra, Jan; Tiuryn, Jerzy 84c:03069 Implicit definability of algebraic structures by means of program properties. Fund. Inform. 4 (1981), no. 3, 661-674.  ... 
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Lambda Calculus with Explicit Recursion

Zena M. Ariola, Jan Willem Klop
<span title="">1997</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/joe2ngto45hbnl3pncnesnq344" style="color: black;">Information and Computation</a> </i> &nbsp;
ACKNOWLEDGMENTS This work was done at the Department of Computer and Information Science of the University of Oregon, at the Department of Software Technology of CWI, and at the Department of Computer  ...  We thank Femke van Raamsdonk and Vincent van Oostrom for introducing us to interaction nets, Stefan Blom for scrutinizing several proofs, and Amr Sabry for stimulating discussions about a draft of this  ...  These calculi should correspond to the intermediate languages used in the compilation of the functional core of both strict and non-strict languages.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/inco.1997.2651">doi:10.1006/inco.1997.2651</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7wfm7qsrknfu5al5yvueolvknm">fatcat:7wfm7qsrknfu5al5yvueolvknm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190418073415/https://core.ac.uk/download/pdf/82558941.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ff/08/ff0887e6bcb46a57428be09843976493ed331ac3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/inco.1997.2651"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Page 756 of Mathematical Reviews Vol. 57, Issue 3 [page]

<span title="">1979</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
the definability theorems of Robinson and Beth.  ...  A class K of structures is called a generalized L(m, n)-implicational class if it is the class of models of a set of universal Horn sentences of the infinitary language L(m, n).  ... 
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Page 791 of Mathematical Reviews Vol. , Issue 2002B [page]

<span title="">2002</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
We present an overview of results concerning the interaction of 22, with least fixed-point logic and first-order implicit definability on finite structures.”  ...  “We also consider the elementary theory of reals in variations of this language in view of quantifier elimination and decidabil- ity and provide positive and negative results for various variant languages  ... 
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Page 6556 of Mathematical Reviews Vol. , Issue 87k [page]

<span title="">1987</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
A logic of inequalities is also investigated and a complete proof system (with one infinitary inference rule) is provided.”  ...  More specifically, a hierarchy of what are called n-rational algebras is defined and some of their mathematical properties are investigated.  ... 
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