Models of weak theories of truth

Models of weak theories of truth In the following paper we propose a model-theoretical way of comparing the “strength” of various truth theories which are conservative over $$ PA $$ P A . Let $${\mathfrak {Th}}$$ Th denote the class of models of $$ PA $$ P A which admit an expansion to a model of theory $${ Th}$$ T h . We show (combining some well known results and original ideas) that $$\begin{aligned} {{\mathfrak {PA}}}\supset {\mathfrak {TB}}\supset {{\mathfrak {RS}}}\supset {\mathfrak {UTB}}\supseteq \mathfrak {CT^-}, \end{aligned}$$ PA ⊃ TB ⊃ RS ⊃ UTB ⊇ CT - , where $${\mathfrak {PA}}$$ PA denotes simply the class of all models of $$ PA $$ P A and $${\mathfrak {RS}}$$ RS denotes the class of recursively saturated models of $$ PA $$ P A . Our main original result is that every model of $$ PA $$ P A which admits an expansion to a model of $$ CT ^-$$ C T - , admits also an expansion to a model of $$ UTB $$ U T B . Moreover, as a corollary to one of the results (brought to us by Carlo Nicolai) we conclude that $$ UTB $$ U T B is not relatively interpretable in $$ TB $$ T B , thus answering the question from Fujimoto (Bull Symb Log 16:305–344, 2010). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Models of weak theories of truth

Loading next page...
 
/lp/springer_journal/models-of-weak-theories-of-truth-hNPn1n5QHd
Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by The Author(s)
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
D.O.I.
10.1007/s00153-017-0531-1
Publisher site
See Article on Publisher Site

Abstract

In the following paper we propose a model-theoretical way of comparing the “strength” of various truth theories which are conservative over $$ PA $$ P A . Let $${\mathfrak {Th}}$$ Th denote the class of models of $$ PA $$ P A which admit an expansion to a model of theory $${ Th}$$ T h . We show (combining some well known results and original ideas) that $$\begin{aligned} {{\mathfrak {PA}}}\supset {\mathfrak {TB}}\supset {{\mathfrak {RS}}}\supset {\mathfrak {UTB}}\supseteq \mathfrak {CT^-}, \end{aligned}$$ PA ⊃ TB ⊃ RS ⊃ UTB ⊇ CT - , where $${\mathfrak {PA}}$$ PA denotes simply the class of all models of $$ PA $$ P A and $${\mathfrak {RS}}$$ RS denotes the class of recursively saturated models of $$ PA $$ P A . Our main original result is that every model of $$ PA $$ P A which admits an expansion to a model of $$ CT ^-$$ C T - , admits also an expansion to a model of $$ UTB $$ U T B . Moreover, as a corollary to one of the results (brought to us by Carlo Nicolai) we conclude that $$ UTB $$ U T B is not relatively interpretable in $$ TB $$ T B , thus answering the question from Fujimoto (Bull Symb Log 16:305–344, 2010).

Journal

Archive for Mathematical LogicSpringer Journals

Published: Apr 22, 2017

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off