Definability of satisfaction in outer models

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Definability of satisfaction in outer models

Original language description

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 In the appendix, we review some unpublished results of Mack Stanley which are directly related to our topic.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2016

Confidentiality

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

Name of the periodical

Journal of Symbolic Logic

ISSN

0022-4812

e-ISSN

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Volume of the periodical

81

Issue of the periodical within the volume

3

Country of publishing house

US - UNITED STATES

Number of pages

22

Pages from-to

1047-1068

UT code for WoS article

000384284500016

EID of the result in the Scopus database

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