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Almost free groups and Ehrenfeucht-Fraïssé games for successors of singular cardinals
[article]

2002
*
arXiv
*
pre-print

We strengthen non-structure theorems

arXiv:math/0212063v1
fatcat:ozvuznpggbejtnzadwajefjfii
*for**almost**free*Abelian*groups*by studying long*Ehrenfeucht*-*Fraisse**games*between a fixed*group**of**cardinality*lambda*and*a*free*Abelian*group*. ... We prove*for*a large set*of**successor**cardinals*lambda=mu^+ existence*of*nonfree (mu*omega_1)-*game*-*free**groups**of**cardinality*lambda. We concentrate on*successors**of**singular**cardinals*. ...*For*an ordinal ǫ, a*group*G is called ǫ-*game*-*free*, if the "isomorphism player" has a winning strategy in the*Ehrenfeucht*-*Fraïssé**game**of*length ǫ between G*and*a*free*Abelian*group*(countable many elements ...##
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Almost free groups and Ehrenfeucht–Fraı̈ssé games for successors of singular cardinals

2002
*
Annals of Pure and Applied Logic
*

We strengthen nonstructure theorems

doi:10.1016/s0168-0072(02)00037-4
fatcat:upvdjksw7rg7jhuh5btpf5h3by
*for**almost**free*Abelian*groups*by studying long*Ehrenfeucht*-Fra ssà e*games*between a ÿxed*group**of**cardinality**and*a*free*Abelian*group*. ... We prove*for*a large set*of**successor**cardinals*= + the existence*of*nonfree ( · !1)-*game*-*free**groups**of**cardinality*. We concentrate on*successors**of**singular**cardinals*. (S. ... On cub-*game**and**game*-*free**groups*In this section, is a*singular**cardinal*, Ä denotes the coÿnality*of*,*and*is the*successor**cardinal**of*. ...##
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Page 5727 of Mathematical Reviews Vol. , Issue 2003h
[page]

2003
*
Mathematical Reviews
*

Stoyan Nedev (BG-AOS; Sofia)
2003h:03073 03E05 03C75 20K20
Shelah, Saharon (IL-HEBR-IM; Jerusalem) ;
Vaisinen, Pauli (FIN-HELS; Helsinki)

*Almost**free**groups**and**Ehrenfeucht*-*Fraissé**games**for**successors*... A /-*free**group**of**cardinality*/ is called*almost**free*. The first author proved that an*almost**free**group**of**singular**cardinality*is*free*. ...##
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Weak Ehrenfeucht-Fraïssé games

2011
*
Transactions of the American Mathematical Society
*

We investigate determinacy

doi:10.1090/s0002-9947-2011-05222-0
fatcat:xshduwvfknhahicyfm56tt5mpy
*of*the weak EF-*game**for*different α (the length*of*the*game*)*and*its relation to the ordinary EF-*game*. ... Thus the difference between this*and*the ordinary*Ehrenfeucht*-*Fraïssé**game*is that the isomorphism can be arbitrary, whereas in the ordinary EF-*game*it is determined by the moves*of*the players. ... An*almost**free**group*is such a*group*that all its countable subgroups (or more generally, all subgroups*of*size < κ*for*κ an uncountable*cardinal*) are*free*,*and*similarly*for**free**and**almost**free*abelian ...##
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The Ehrenfeucht-Fraisse-game of length omega_1
[article]

1993
*
arXiv
*
pre-print

This

arXiv:math/9305204v1
fatcat:pcjkyiee6jaejapovvti2zgefu
*game*is like the ordinary*Ehrenfeucht*-*Fraisse*-*game**of*L_omega omega except that there are omega_1 moves. It is clear that G_omega_1(A,B) is determined if A*and*B are*of**cardinality*<= aleph_1. ... Let (A)*and*(B) be two first order structures*of*the same vocabulary. We shall consider the*Ehrenfeucht*-*Fraisse*-*game**of*length omega_1*of*A*and*B which we denote by G_omega_1(A,B). ... Therefore, if G ω 1 (A, B) is determined*for*all*almost**free**groups*A*and*B*of**cardinality*ℵ 2 , then ω 2 is Mahlo in L. ...##
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The Ehrenfeucht-Fraisse-Game of Length ω 1

1993
*
Transactions of the American Mathematical Society
*

This

doi:10.2307/2154287
fatcat:o5fevwx25zggvbovajp5pzcxmi
*game*is like the ordinary*Ehrenfeucht*-*Fraïssé*-*game**of*L ωω except that there are ω 1 moves. It is clear that G ω 1 (A, B) is determined if A*and*B are*of**cardinality*≤ ℵ 1 . ... Let A*and*B be two first order structures*of*the same vocabulary. We shall consider the*Ehrenfeucht*-*Fraïssé*-*game**of*length ω 1*of*A*and*B which we denote by G ω 1 (A, B) . ... Therefore, if G ω 1 (A, B) is determined*for*all*almost**free**groups*A*and*B*of**cardinality*ℵ 2 , then ω 2 is Mahlo in L. ...##
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Constructing strongly equivalent nonisomorphic models for unstable theories

1991
*
Annals of Pure and Applied Logic
*

If T is an unstable theory

doi:10.1016/0168-0072(91)90031-g
fatcat:badcvfs4jbgk7ishcpvxbng6cy
*of**cardinality*o (d > w, in the superstable with DOP case) is regular*and*A<* = h, then we construct*for*T strongly equivalent nonisomorphic models*of**cardinality*1. ... Hyttinen, T.*and*H. Tuuri, Constructing strongly equivalent nonisomorphic models*for*unstable theories, Annals*of*Pure*and*Applied Logic 52 (1991) 203-248. ... The authors would also like to thank Juha Oikkonen, Taneli Huuskonen*and*Lauri Hella*for*their insights*and*inspiring discussions, Bradd Hart*for*his valuable help*and*Daniel Lascar*for*teaching stability ...##
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Laver and set theory

2016
*
Archive for Mathematical Logic
*

In this commemorative article, the work

doi:10.1007/s00153-015-0462-7
fatcat:5ziwvh27arbprhsdlmku4f2npe
*of*Richard Laver is surveyed in its full range*and*extent. ... Doctoral students*of*Richard Laver Stephen Grantham, An analysis*of*Galvin In addition to having these doctoral students at Boulder, Laver was on the thesis committees*of*, among many: ... Then in 1947 Roland*Fraïssé*, now best known*for*the*Ehrenfeucht*-*Fraïssé**games**and**Fraïssé*limits, pointed to basic issues*for*countable order types in four conjectures. ...##
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Page 107 of Mathematical Reviews Vol. , Issue Index
[page]

*
Mathematical Reviews
*

(English summary) 2003e:03091
Shelah, Saharon (with Vaisénen, Pauli)

*Almost**free**groups**and**Ehrenfeucht*-*Fraissé**games**for**successors**of**singular**cardinals*. ... .) **Almost**free*modules. 2003e:20002 Goldstern, Martin R. (with Shelah, Saharon) Clones on regular*cardinals*. ...##
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Page 2275 of Mathematical Reviews Vol. , Issue Index
[page]

*
Mathematical Reviews
*

(From the text) 2004g:03072 03504
AUTHOR INDEX
Shelah
— (with Hyttinen, Tapani; Vaananen, Jouko) More on the

*Ehrenfeucht*-*Fraissé**game**of*length w;. (English summary) Fund. ... (Howard Smith) 2004j:20074 20F19 (20E25) —*Successor**of**singulars*: combinatorics*and*not collapsing*cardinals*< « in (< «)-support iterations. (English summary) /srael J. Math. 134 (2003), 127-155. ...##
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Algebraic logic and topoi; a philosophical holistic approach

2020
*
International Journal of Algebra
*

*For*example topoi

*and*category theory are approached as means to unify apparently scattered results in the literature. ... the number

*of*subvarieties

*of*RCA ω which is reminiscent

*of*Shelah's stability theory

*and*the interaction

*of*algebraic logic

*and*descriptive set theory as means to approach Vaught's conjecture in model ... his winning strategy from the private

*Ehrenfeucht*-

*Fraïssé*forth

*game*, to the graph

*game*on At f = At(A n+1,n ) [26, p 841] forcing a win using 2n nodes. ...

##
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Page 1899 of Mathematical Reviews Vol. , Issue Index
[page]

*
Mathematical Reviews
*

(Judith Roitman) 2003c:03091 03E40 (03G05, 06E05)
— (with Vaisanen, Pauli)

*Almost**free**groups**and**Ehrenfeucht*-*Fraissé**games**for**successors**of**singular**cardinals*. (English summary) Ann. Pure Appl. ... A QFT procedure*for*generating design frequencies*and*bounds*of*guaranteed accuracy. (English summary) Reliab. ...##
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Can we classify complete metric spaces up to isometry?
[article]

2017
*
arXiv
*
pre-print

The results concerning non-separable spaces (

arXiv:1610.01750v2
fatcat:vcyvmnnygfdw5ctzpss4azplpe
*and*, to some extent, the setup*and*techniques used to handle them) are instead new,*and*suggest new lines*of*investigation in this area*of*research. ... We survey some old*and*new results concerning the classification*of*complete metric spaces up to isometry, a theme initiated by Gromov, Vershik*and*others. ... κ-branches,*and*winning strategies in the corresponding dynamic*Ehrenfeucht*-*Fraïssé**games*(this yields a neat analog*of*the notion*of*Scott watershed from the Scott analysis*of*countable models, see ...##
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The structure of graphs and new logics for the characterization of Polynomial Time
[article]

2017

Our exposition provides evidence that rank logics are a natural object to study

doi:10.18452/16335
fatcat:f6rgrxx2hfghdfse7o75hpai7a
*and*establishes the most expressive*of*our rank logics as a viable candidate*for*capturing PTIME, suggesting that rank logics ... First, we adapt a representation-invariant, singly exponential-time graph canonization algorithm*of*Corneil*and*Goldberg (1984)*and*conclude that on structures whose relations are*of*arity at most 2, the ...*Ehrenfeucht*-*Fraïssé*style pebble*games*,*for*example, are typically played by two players: spoiler*and*duplicator. ...