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Easy Proofs of Löwenheim-Skolem Theorems by Means of Evaluation Games
[article]

2015
*
arXiv
*
pre-print

We propose a

arXiv:1507.03665v1
fatcat:sp3b3jedjfdk5i24sipoox75ui
*proof**of*the downward L\"owenheim-*Skolem*that relies on strategies deriving from*evaluation**games*instead*of*the*Skolem*normal forms. ... the one*of*an*evaluation**game*. ...*Löwenheim*-*Skolem**theorem*. ...##
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Lectures on Jacques Herbrand as a Logician
[article]

2014
*
arXiv
*
pre-print

Besides Herbrand's Fundamental

arXiv:0902.4682v5
fatcat:pgxxo7vjcbeyvhjej4svsv6lqe
*Theorem*and its relation to the Loewenheim-*Skolem*-*Theorem*, we carefully investigate Herbrand's notion*of*intuitionism in connection with his notion*of*falsehood in an infinite ... We sketch Herbrand's two*proofs**of*the consistency*of*arithmetic and his notion*of*a recursive function, and last but not least, present the correct original text*of*his unification algorithm with a new ...*of*this paper. ...##
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On synthesizing Skolem functions for first order logic formulae
[article]

2022
*
arXiv
*
pre-print

While every

arXiv:2102.07463v2
fatcat:aafbqeoj3zhy3cugbey4gvdqdq
*Skolemized*formula in first-order logic makes use*of**Skolem*constants and/or functions, not all such*Skolem*constants and/or functions admit effectively computable interpretations. ... In this paper, we investigate the computability*of**Skolem*functions and their automated synthesis in the full generality*of*first order logic. ...*Löwenheim*-*Skolem**theorem*. ...##
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The Development of Mathematical Logic from Russell to Tarski, 1900–1935
[chapter]

2009
*
The Development of Modern Logic
*

This is the

doi:10.1093/acprof:oso/9780195137316.003.0029
fatcat:ygiplet5oraf7fza6fsmf5j5ly
*Löwenheim*-*Skolem**theorem*. ... Herbrand's*Theorem*can thus be seen as giving finitary*meaning*to the*Löwenheim*-*Skolem**theorem*. Let us now give a brief outline*of*the*theorem*. ...##
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First-order logic with self-reference
[article]

2022
*
arXiv
*
pre-print

We also argue for the naturalness and benefits

arXiv:2207.07397v1
fatcat:rxfau7u7sffcbm4mxtwlmlyche
*of*the investigated approach to recursion and self-reference*by*, for example, relating the new logics to Lindstrom's Second*Theorem*. ... For example, the validity problems*of*the two-variable fragments*of*the logics are shown coNexpTime-complete, which is in stark contrast with the high undecidability*of*two-variable logic extended with ... In the case*of*SCL it turns out that we can adapt the standard*proof*that FO has the countable downwards*Löwenheim*-*Skolem*property.*Theorem*6.2. Let ϕ be a sentence*of*SCL and suppose that A |= ϕ. ...##
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A Finitary Analogue of the Downward Löwenheim-Skolem Property
[article]

2017
*
arXiv
*
pre-print

We present a model-theoretic property

arXiv:1705.04493v1
fatcat:w646656oprfgdedxsard2ti2im
*of*finite structures, that can be seen to be a finitary analogue*of*the well-studied downward*Löwenheim*-*Skolem*property from classical model theory. ... We conclude*by*presenting a strengthening*of*L-EBSP, that asserts "logical self-similarity at all scales" for a suitable notion*of*scale. ...*of*the downward*Löwenheim*-*Skolem**theorem*that is "intermediate" between the versions*of*this*theorem**by**Skolem*and Mal'tsev. ...##
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Quantified Constraints and Containment Problems

2015
*
Logical Methods in Computer Science
*

We further show the exponent's bound |A|^|B| to be close to tight

doi:10.2168/lmcs-11(3:9)2015
fatcat:mgjtfhpasrewzm2dwh3kbtsl24
*by*giving a sequence*of*structures A together with a fixed B, |B|=2, such that there is a surjective homomorphism from A^r to B only when ... In the final part*of*the paper we ponder a notion*of*Q-core that is some canonical representative among the class*of*templates that engender the same QCSP. ... Acknowledgements We are very grateful to Arnaud Durand for supplying the undecidability*proof**of*the entailment problem for positive FO. ...##
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Quantified Constraints and Containment Problems

2008
*
Logic in Computer Science
*

We note that this condition is already necessary to guarantee containment

doi:10.1109/lics.2008.15
dblp:conf/lics/ChenMM08
fatcat:shnqvf2vyngyvivpbsz7oifloy
*of*the Π 2 restriction*of*QCSP, that is Π 2 -CSP(A) ⊆ Π 2 -CSP(B). ... That is, given two sentences ϕ and ψ*of*first-order logic with no instances*of*negation or disjunction, we give an algorithm that determines whether ϕ → ψ is true in all structures (models). ... Acknowledgements We are very grateful to Arnaud Durand for supplying the undecidability*proof**of*the entailment problem for positive FO. ...##
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Equilibrium semantics of languages of imperfect information

2010
*
Annals of Pure and Applied Logic
*

In this approach, coined equilibrium semantics, the value

doi:10.1016/j.apal.2009.07.019
fatcat:izg7yevkyfadjcvdoypqzrhenq
*of*an IF sentence on a particular structure is determined*by*the expected utility*of*the existential player in any*of*the game's equilibriums. ... We prove that each rational number can be realized*by*an IF sentence. We also give a lower and upper bound on the expressive power*of*IF logic under equilibrium semantics. ... Acknowledgments We are much indebted to the reviewers for many excellent technical and nontechnical suggestions and to Jakub Szymanik for pointing out the recent work*by*Galliani. ...##
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On modal logics of model-theoretic relations
[article]

2019
*
arXiv
*
pre-print

We prove a downward

arXiv:1804.09810v4
fatcat:4ta7oth5zbdsblofpzdihiw6wy
*Löwenheim*–*Skolem**theorem*for first-order language expanded with the modal operator for the extension relation between models. ... Given a class C*of*models, a binary relation R between models, and a model-theoretic language L, we consider the modal logic and the modal algebra*of*the theory*of*C in L where the modal operator is interpreted ... The work on this paper was supported*by*the Russian Science Foundation under grant 16-11-10252 and carried out at Steklov Mathematical Institute*of*Russian Academy*of*Sciences. ...##
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On the relative consistency strength of determinacy hypotheses

1985
*
Transactions of the American Mathematical Society
*

A variant

doi:10.1090/s0002-9947-1985-0787961-2
fatcat:am6k3agb4nelvmalr3ezefgssu
*of*the usual*proof**of*the*Skolem*-*Löwenheim**theorem*shows that X < sup< £: There is a surjection tr: R -> £ >.*Theorem*2.3. ... So*by**Skolem*-*Löwenheim*Vz3>> >rz3# < aAL»[y] •= ZFn + AC + _,OD-DET). ...##
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On Semantic Generalizations of the Bernays-Schönfinkel-Ramsey Class with Finite or Co-finite Spectra
[article]

2010
*
arXiv
*
pre-print

Our study provides alternative

arXiv:1002.4334v2
fatcat:erzc5b3h45cnhnoxwbctygb3ou
*proofs**of*interesting results like the Loś-Tarski*Theorem*and the semantic subsumption*of*the*Löwenheim*class with equality*by*BSR. ... Motivated*by*model-theoretic properties*of*the BSR class, we present a family*of*semantic classes*of*FO formulae with finite or co-finite spectra over a relational vocabulary Σ. ... Then if Φ has models*of*unbounded domain-size -which is iff it has an infinite model -then*by*the previous statement and the Upward and Downward*Löwenheim*-*Skolem**theorems*, it has models*of*all domain- ...##
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Logical queries over views

2010
*
ACM Transactions on Computational Logic
*

known as the

doi:10.1145/1656242.1656243
fatcat:vv2spm7q6fgmdegb7kdbwwn3ve
*Löwenheim*class. ...*By*expanding the view definitions, every first-order view query can clearly be rewritten to eliminate the views. ... [If it is infinite,*by*the*Löwenheim*-*Skolem**theorem*, we may assume that it is countable.] ...##
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Expressiveness of the modal mu-calculus on monotone neighborhood structures
[article]

2015
*
arXiv
*
pre-print

We characterize the expressive power

arXiv:1502.07889v1
fatcat:gafhmhfk4fef3hr73rvrzqgpv4
*of*the modal mu-calculus on monotone neighborhood structures, in the style*of*the Janin-Walukiewicz*theorem*for the standard modal mu-calculus. ... Our main result shows that the monotone modal mu-calculus corresponds exactly to the fragment*of*this second-order language that is invariant for neighborhood bisimulations. ... Let κ be the smallest*Löwenheim*-*Skolem*number for µNML g , so that κ has the property described in the previous lemma. ...##
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Some classical model theoretic aspects of bounded shrub-depth classes
[article]

2020
*
arXiv
*
pre-print

We show that this class satisfies an extension

arXiv:2010.05799v1
fatcat:fpco5dvxarfi3pegqogcgxbjym
*of*the classical*Löwenheim*-*Skolem*property into the finite and for MSO. ... The*proof*for the last*of*these is via an adaptation*of*the*proof**of*the classical Lindström's*theorem*characterizing FO over arbitrary structures. ... I also thank Anand Pillay for pointing me to [12] for the*proof**of*Lindström's*theorem*. ...
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