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- 22:27, 20 November 2014 Short recursively saturated models and boundedly saturated models (hist) [2,375 bytes] Eshochat (Talk | contribs) (Created page with " == Short Recursively Saturated Models == A model is short if there is an element in the model whose Skolem closure is cofinal in the model. That is, M is short iff there i...")
- 11:10, 25 May 2014 Bibtex (hist) [28,205 bytes] WikiSysop (Talk | contribs) (Created page with "@article {coskeykossak2010:thecomplexity, AUTHOR = {Coskey, Samuel and Kossak, Roman}, TITLE = {The complexity of classification problems for models of ...")
- 06:47, 20 June 2013 Integer parts of real closed fields (hist) [479 bytes] Rkossak (Talk | contribs) (Created page with " == Tennenbaum property == Je\v{z}\'abek and Ko{\l}odziejczyk show")
- 06:44, 20 June 2013 Model theory of weak fragments of arithmetic (hist) [40 bytes] Rkossak (Talk | contribs) (Created page with "Integer parts of real closed fields.")
- 08:53, 7 February 2013 Automorphism groups in general (hist) [352 bytes] Jschmerl (Talk | contribs) (Created page with "== Rigid models == A model $M$ is '''rigid''' if ${\rm Aut}(M)$ is trivial -- that is, its only automorphism is the identity function. Every model of PA has a rigid elementary ...")
- 15:34, 6 February 2013 Automoprhism groups (hist) [104 bytes] Rkossak (Talk | contribs) (Created page with "Automorphism groups in general. Automorphisms groups of countable recursively saturated models.")
- 12:39, 23 January 2013 Nonstandard satisfaction classes (hist) [2,446 bytes] Rkossak (Talk | contribs) (Created page with "== Fullness of $M$ == A satisfaction class for a model $M$ is $e$-full, if $S$ decides all If for every $\Sigma_e$ sentence (in the sense of $M$) $\varphi$ with parameters eith...")
- 12:38, 23 January 2013 Uncountable models with interesting second-order properties (hist) [3,885 bytes] Rkossak (Talk | contribs) (Created page with " == Friedman's 14th problem == Let $T$ be a completion of PA. Let ${\rm Ot}(T)$ be the spectrum of order types of nonstandard models of $T$. In <cite> friedman1975:onehundred ...")
- 12:34, 23 January 2013 Lattices of elementary substructures (hist) [2,664 bytes] Rkossak (Talk | contribs) (Created page with "For $M\models PA$ let ${\rm{Lt}(M)}=(\{K: K\prec M\},\prec)$ and for $M\prec N$, let ${\rm Lt}(N/M)=(\{K: M\prec K\prec M\},\prec)$. In general, the lattice problem is: Which l...")
- 12:32, 23 January 2013 Standard systems and the Scott set problem (hist) [1,135 bytes] Rkossak (Talk | contribs) (Created page with " == The Scott set problem == A Scott set is a set of sets of natural numbers $\mathfrak X$ such that $(\omega, {\mathfrak X})\models {\sf WKL}_0$, Assume $\lnot{\sf CH}$. Is ev...")
- 12:28, 23 January 2013 Recursively saturated, resplendent models, and saturated models (hist) [333 bytes] Rkossak (Talk | contribs) (Created page with "Cuts in recursively saturated models. Automorphisms of countable recursively saturated models. Automorphisms groups of countable recursively saturated models. [[En...")
- 17:31, 22 January 2013 Resplendent models (hist) [2,020 bytes] Rkossak (Talk | contribs) (Created page with " == Gentle expansions == This problem is not directly about models of PA, but is motivated by results concerning maximal automorphisms, first proved in the context of arithmetica...")
- 15:31, 20 January 2013 Library (hist) [430 bytes] WikiSysop (Talk | contribs) (Created page with "{{DISPLAYTITLE: The Peano's parlour library}} Welcome to the library, our central repository for references cited here on Peano's parlour. == Library holdings == <!-- Ple...")
- 12:27, 18 January 2013 Nonstandard satisfaction classes. (hist) [2,446 bytes] Rkossak (Talk | contribs) (Created page with " == Fullness of $M$ == A satisfaction class for a model $M$ is $e$-full, if $S$ decides all If for every $\Sigma_e$ sentence (in the sense of $M$) $\varphi$ with parameters eit...")
- 12:00, 18 January 2013 End extensions, cofinal extensions (hist) [3,090 bytes] Rkossak (Talk | contribs) (Created page with " == Isolated gaps == For $a\in M\models PA$, the gap of $a$, ${\rm gap}(a)$ is $\bigcap\{K_prec_{end} M: a\in K\land \}\setminus \bugcup\{K_prec_{end} M: a\notin K\}$.")
- 10:22, 18 January 2013 Cuts in recursively saturated models (hist) [1,410 bytes] Rkossak (Talk | contribs) (Created page with "== Free cuts == A cut $I$ in a model $M\models PA$ is ''free'' if for all $a, b\in I$ if $(M,a)\equiv (M,b)$, then $(M,I,a)\equiv (M,I,b)$. There are free elementary cuts in ev...")
- 10:01, 18 January 2013 Kanovei's question (hist) [0 bytes] Rkossak (Talk | contribs) (Created page with "Is there a Borel model $M\models PA$ such that the standard system of $M$ is the power set of $\omega$?")
- 09:57, 18 January 2013 Rigid models (hist) [0 bytes] Rkossak (Talk | contribs) (Created page with "There are $\aleph_1$-like rigid models of $PA$. Two different constructions are given in Kossak; Schmerl, ''Minimal satisfaction classes with an application to rigid models of ...")
- 09:46, 18 January 2013 Automorphisms of countable recursively saturated models (hist) [1,401 bytes] Rkossak (Talk | contribs) (Created page with " == Extending automorphisms == Let $G$ be the automorphism group of a countable recursively saturated model of $PA$. For every nontrivial $f\in G$ there is a countable recursiv...")
- 09:37, 18 January 2013 Complexity and classification of countable models (hist) [2,038 bytes] Rkossak (Talk | contribs) (Created page with " == Borel classification questions == Let $T$ be a completion of $PA$. It is not hard to see that the isomorphism problem for finitely generated models of $T$, $\cong^{fg}_T$, i...")
- 17:05, 17 January 2013 Saturated models (hist) [1,312 bytes] Rkossak (Talk | contribs) (Created page with " == The automorphism group == In a recent paper Nurkhaidarov and Schmerl 2011 proved the following: Let $\kappa$ be regular, uncounale, and such that $\kappa^{<\kappa}=\kappa$...")
- 16:52, 17 January 2013 Automorphisms groups of countable recursively saturated models (hist) [3,054 bytes] Rkossak (Talk | contribs) (Created page with " == Generic automorphisms and the small index property == Lascar showed that countable arithmetically saturated models of $PA$ have generic automorphisms and used them to show t...")
- 16:32, 17 January 2013 Jonsson models (hist) [0 bytes] Rkossak (Talk | contribs) (Created page with "A model $\mathfrak B$ is ''J\'onsson'' if $|{\mathfrak B}|>\aleph_0$ and for every ${\mathfrak A}\prec {\mathfrak B}$, if $|{\mathfrak A}|=|{\mathfrak B}|$, then ${\mathfrak A}={...")
- 16:03, 17 January 2013 Rather classless models. (hist) [0 bytes] Rkossak (Talk | contribs) (Created page with " $X\subseteq M\models PA$ is a ''class'' if for all $a\in M$, $\{x\in X: x<a\}$ is definable (coded) in $M$. $M$ is ''rather classless'' if each class of $M$ is definable. Since...")
- 11:45, 17 January 2013 Errata (hist) [9,066 bytes] Rkossak (Talk | contribs) (Created page with "\documentclass[10pt]{article} \usepackage[centertags]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsthm} \title{The Structure of Models of Peano Arithmetic:...")
- 11:40, 17 January 2013 Lattices of elementary substructures. (hist) [2,018 bytes] Rkossak (Talk | contribs) (Created page with "Let $L$ be a lattice. Is $L$ isomorphic to ${\rm{Lt}(M)}=(\{K: K\prec M\},\prec)$, for some $M\models PA$? There is a vast literature on the problem and many special cases re...")
- 11:16, 17 January 2013 The Scott set problem. (hist) [0 bytes] Rkossak (Talk | contribs) (Created page with "A Scott set is a set of sets of natural numbers $\mathfrak X$ such that $(\omega, {\mathfrak X})\models WKL_0$, Assume $\lnot{\sf CH}$. Is every Scott set the standard system of...")
- 11:12, 17 January 2013 Standard systems and the Scott set problem. (hist) [0 bytes] Rkossak (Talk | contribs) (Created page with "1. The Scott set problem.")
- 11:10, 17 January 2013 Friedman's 14-th problem. (hist) [0 bytes] Rkossak (Talk | contribs) (Created page with "Let $T$ be a completion of PA. Let ${\rm Ot}(T)$ be the spectrum of order types of nonstandard models of $T$. Does ${\rm Ot(T)}$ depend on $T$? Friedman, Harvey, One hundred ...")
- 11:03, 17 January 2013 Uncountable models with interesting second-order properties. (hist) [0 bytes] Rkossak (Talk | contribs) (Created page with "1. Friedman's 14-th problem.")
- 10:56, 17 January 2013 Omitting theories of undefinable sets (hist) [0 bytes] Rkossak (Talk | contribs) (Created page with "Suppose $M$ is countable recursively saturated and $X$ is an undefinable subset of $M$. Is there a countable recursively saturated $N$ such that $N$ is an elementary end exten...")
- 14:17, 16 January 2013 Recursively saturated, resplendent models, and saturated models. (hist) [261 bytes] Rkossak (Talk | contribs) (Created page with " == Omitting theories of undefinable sets == Suppose $M$ is countable recursively saturated and $X$ is an undefinable subset of $M$. Is there a countable recursively saturate...")
- 14:07, 16 January 2013 Cuts in models of PA and independence results (hist) [1,709 bytes] Rkossak (Talk | contribs) (Created page with "Nothing here yet")