Definability of satisfaction in outer models

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11210%2F16%3A10336147" target="_blank" >RIV/00216208:11210/16:10336147 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1017/jsl.2016.33" target="_blank" >http://dx.doi.org/10.1017/jsl.2016.33</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/jsl.2016.33" target="_blank" >10.1017/jsl.2016.33</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Definability of satisfaction in outer models

Popis výsledku v původním jazyce

Let M be a transitive model of ZFC. We say that a transitive model of ZFC, N , is an outer model of M if M is a subset of N and the ordinals coincide. The outer model theory of M is the collection of all formulas with parameters from M which hold in all outer models of M (which exist in a universe in which M is countable; this is independent of the choice of such a universe). Satisfaction defined with respect to outer models can be seen as a useful strengthening of first-order logic. Starting from an inaccessible cardinal κ, we show that it is consistent to have a transitive model M of ZFC of size κ in which the outer model theory is lightface definable, and moreover M satisfies V = HOD. The proof combines the infinitary logic L_infinity, omega, Barwise's results on admissible sets, and a new forcing iteration of length strictly less than κ+ which manipulates the continuum function on certain regular cardinals below κ. In the appendix, we review some unpublished results of Mack Stanley which are directly related to our topic.

Název v anglickém jazyce

Definability of satisfaction in outer models

Popis výsledku anglicky

Let M be a transitive model of ZFC. We say that a transitive model of ZFC, N , is an outer model of M if M is a subset of N and the ordinals coincide. The outer model theory of M is the collection of all formulas with parameters from M which hold in all outer models of M (which exist in a universe in which M is countable; this is independent of the choice of such a universe). Satisfaction defined with respect to outer models can be seen as a useful strengthening of first-order logic. Starting from an inaccessible cardinal κ, we show that it is consistent to have a transitive model M of ZFC of size κ in which the outer model theory is lightface definable, and moreover M satisfies V = HOD. The proof combines the infinitary logic L_infinity, omega, Barwise's results on admissible sets, and a new forcing iteration of length strictly less than κ+ which manipulates the continuum function on certain regular cardinals below κ. In the appendix, we review some unpublished results of Mack Stanley which are directly related to our topic.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Symbolic Logic

ISSN

0022-4812

e-ISSN

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Svazek periodika

81

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

1047-1068

Kód UT WoS článku

000384284500016

EID výsledku v databázi Scopus

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