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Full satisfaction classes, definability, and automorphisms
[article]
2021
arXiv
pre-print
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In particular, the automorphism group of a model expanded with a satisfaction class is never equal to the automorphism group of the original model. ...
It follows that in every such model, there exists a full satisfaction class which makes every element definable and thus the expanded model is minimal and rigid. ...
Acknowledgements This research was supported by an NCN MAESTRO grant 2019/34/A/HS1/00399 "Epistemic and Semantic Commitments of Foundational Theories." ...
arXiv:2104.09969v1
fatcat:mnoaudy3yzbf7oxd67pnqtunma
Page 4134 of Mathematical Reviews Vol. , Issue 92h
[page]
1992
Mathematical Reviews
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Constantin Milici (Timisoara)
92h:03051 03C62
Kossak, Roman (PL-PAN); Schmerl, James H. (1-CT)
Minimal satisfaction classes with an application to rigid models of Peano arithmetic.
Notre Dame J. ...
The result is based on a theorem saying that every countable recursively saturated model of PA has minimal inductive satisfac- tion classes. A generalization to x-like models is also given. ...
Carnap's Early Semantics
2012
Erkenntnis: An International Journal of Scientific Philosophy
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der Logistik. 123 The main innovation in the 1936 paper is its application
to formal models with the aim to classify different limiting types of model structures defined
by an AS: 'minimal structures ...
a categorical (in Carnap's terms "monomorphic") axiomatization. 236 In the case of Peano arithmetic, adding an accessibility axiom or a minimal axiom to the base system enforces model minimality on the ...
doi:10.1007/s10670-012-9365-8
fatcat:7jcctf5ajfdhlnshex7iaruija
SET THEORY FROM CANTOR TO COHEN
[chapter]
2009
Philosophy of Mathematics
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What follows is an account of the development of set theory from its beginnings through the creation of forcing based on these contentions, with an avowedly Whiggish emphasis on the heritage that has been ...
With the emergence of the cumulative hierarchy picture, set theory can be regarded as becoming a theory of well-foundedness, later to expand to a study of consistency strength. ...
ACKNOWLEDGEMENTS This is a revision with significant changes of the author's The Mathematical Development of Set Theory from Cantor to Cohen, The Bulletin of Symbolic Logic, volume 2, 1996, pages 1-71, ...
doi:10.1016/b978-0-444-51555-1.50014-6
fatcat:vnj2vdlpofdp7pg37tyiemdkiq
Set Theory from Cantor to Cohen
[chapter]
2012
Handbook of the History of Logic
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What follows is an account of the development of set theory from its beginnings through the creation of forcing based on these contentions, with an avowedly Whiggish emphasis on the heritage that has been ...
With the emergence of the cumulative hierarchy picture, set theory can be regarded as becoming a theory of well-foundedness, later to expand to a study of consistency strength. ...
ACKNOWLEDGEMENTS This is a revision with significant changes of the author's The Mathematical Development of Set Theory from Cantor to Cohen, The Bulletin of Symbolic Logic, volume 2, 1996, pages 1-71, ...
doi:10.1016/b978-0-444-51621-3.50001-3
fatcat:ogdmpb6mlvgxbdvoh3jqq6umqe
Chapter 1 Pure computable model theory
[chapter]
1998
Studies in Logic and the Foundations of Mathematics
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orders, Peano arithmetic, true arithmetic, and the theory of Boolean algebras. ...
The generalization of the definition of a particular computable algebraic structure to an arbitrary model yields one of the basic concepts of pure computable model theory, an area of logic developed in ...
I thank Tim McNicholl for proofreading parts of an early draft. I thank Graeme Bailey for technical assistance with word-processing. ...
doi:10.1016/s0049-237x(98)80002-5
fatcat:mktikwmmazgale5ejrpnihv6hm
ON THE RELATIONSHIP BETWEEN PLANE AND SOLID GEOMETRY
2012
The Review of Symbolic Logic
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In this paper our major concern is with methodological issues of purity and thus we treat the connection to other areas of the planimetry/stereometry relation only to the extent necessary to articulate ...
To raise the issue of the relation between these two areas brings with it a host of different problems that pertain to mathematical practice, epistemology, semantics, ontology, methodology, and logic. ...
But it was Pieri's fellow countryman Peano who seems to have been the first to find a model of the plane in which Desargues' theorem fails, in an 1894 essay Peano [1894] . ...
doi:10.1017/s1755020312000020
fatcat:ycxnc4ue4rgivjm5chzumj3sfu
Algebras, Projective Geometry, Mathematical Logic, and Constructing the World: Intersections in the Philosophy of Mathematics of A. N. Whitehead
2002
Historia Mathematica
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By then his interests had switched to educational issues, and especially to space and time and relativity theory, where his earlier dependence upon logic was extended to an ontology of events and to a ...
Then in the 1900s he joined Bertrand Russell in an attempt to ground many parts of mathematics in the newly developing mathematical logic. ...
On model-theoretic aspects of basic notions such as number, zero, and successor in the Peano axioms for arithmetic "might be fitted on to anything. B. Russell doesn't seem to object to this." ...
doi:10.1006/hmat.2002.2356
fatcat:af6uawrpibccjgnkqln5ftaism
On the methodology of informal rigour: set theory, semantics, and intuitionism
[article]
2021
arXiv
pre-print
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In an appendix, we also offer briefer reconstructions of Kreisel's attempts to apply informal rigour to the discovery of set theoretic axioms, the distinction between standard and nonstandard models of ...
We conclude by offering a comparison of Kreisel's understanding of informal rigour with Carnap's method of explication. ...
such as first-order Peano arithmetic [PA] . ...
arXiv:2104.14887v1
fatcat:bxlwnrcqizecvfggmwkccchbxu
The Value-Passing Calculus
[chapter]
2013
Lecture Notes in Computer Science
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The logical expression ϕ must be evaluated in the model before process (1) fires an action. If ϕ contains free variables, the evaluation is done with respect to an assignment. ...
A valuepassing calculus consists of a first order theory with boolean completeness and an operational model that makes use of the terms and the boolean expressions of the theory. ...
Section 7 applies the methodology to the value-passing calculus VPC defined over the Peano arithmetics. The model is shown to be minimal among all the Turing complete value-passing calculi. ...
doi:10.1007/978-3-642-39698-4_11
fatcat:ec74pnvkovgelgyuecc34avjm4
Page 81 of Mathematical Reviews Vol. 28, Issue Index
[page]
Mathematical Reviews
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recursively saturated models of Peano arithmetic. ...
A reflection principle and its applications to nonstandard models. 96m:03025
— PA(aa). ...
Answer Set Programming's Contributions to Classical Logic
[chapter]
2011
Lecture Notes in Computer Science
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In this paper, a look at different aspects of ASP, in an effort to identify precisely the limitations of classical logic that they exposed and investigate how the ASP approaches can be transferred back ...
to the classical setting. ...
A (very) early example of this is Peano arithmetic, Peano's standard second order theory of the natural numbers where σ = {0, S/1}. ...
doi:10.1007/978-3-642-20832-4_2
fatcat:yrydik5mlrgmxd7azmhpuudz7i
POLYMORPHISM AND THE OBSTINATE CIRCULARITY OF SECOND ORDER LOGIC: A VICTIMS' TALE
2018
Bulletin of Symbolic Logic
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to Russell's and Poincaré's 1906 "vicious circle" diagnosis. ...
for the intuitionistic type theory with a type of all types (shown inconsistent by Girard's paradox).The comparison suggests that the question of the circularity of second order logic cannot be reduced ...
by Gödel, and essentially corresponding to first-order Peano Arithmetics. ...
doi:10.1017/bsl.2017.43
fatcat:q3xtgurssnhrfmsgieso3aqhe4
A survey of homogeneous structures
2011
Discrete Mathematics
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The article discusses connections between these topics, with an emphasis on examples, and on special properties of an amalgamation class which yield important consequences for the automorphism group. language ...
Recently there has been a focus on connections to topological dynamics, and to constraint satisfaction. ...
An existential interpretation is one in which all the defining formulas can be taken to be existential; similarly for positive existential interpretation, and p.p. interpretation. ...
doi:10.1016/j.disc.2011.01.024
fatcat:fqpfnc25hjdajekkiyaeszw6ye
MODALITY AND AXIOMATIC THEORIES OF TRUTH I: FRIEDMAN-SHEARD
2014
The Review of Symbolic Logic
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First, we show that Modal Friedman-Sheard preserves theoremhood modulo translation with respect to modal operator logic. ...
The idea of this strategy is to develop modal theories over axiomatic theories of truth. ...
F S based on the standard model of arithmetic. ...
doi:10.1017/s1755020314000057
fatcat:nmejpurlmjfi7lwmpojw3c6bh4
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