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Results tagged with model-theory
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user 20597
Model theory is the branch of mathematical logic which deals with the connection between a formal language and its interpretations, or models.
2
votes
Is V, the Universe of Sets, a fixed object?
I believe the answer to your question revolves around correcting a subtle confusion between classes and sets in the Cumulative Hierarchy. This can be shown by reference to Samuel Coskey's Senior Thes …
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2
votes
0
answers
323
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The universe and multiverse views of set theory from the perspective of $ZFC^2$
(Note: the 'Second-order $ZFC$' ($ZFC^2$) I am talking about is the theory [in the second order language of set theory consisting of a single non-logical symbol $\in$ ] consisting of the axioms Exte …
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1
vote
1
answer
226
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Is there a 'Constructible Universe' that is a submodel of a non-transitive model of $ZF$?
In Barwise's book, Admissible Sets and Structures, the following statement is made (on pg. 8):
"...if $ZF$ is consistent, so is $ZF$ + "There is no transitive model of $ZF$"
He mentions this fac …
- 6,132
1
vote
Are there first order theories of interest to an algebraist or at least a model theorist of ...
You might want to take a look at pp.1-2 (and the top quarter of pg. 3) of Harvey Friedman's paper "Restrictions and Extensions" (the rest of the paper (the paper is all of six pages) deals with the sy …
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11
votes
Has decidability got something to do with primes?
You might be interested in A. Grzegorczyk's paper "Undecidability without arithmetization." (Studia Logica, 79(2): 163-230, 2005) in which he dispenses with arithmetization altogether (but does not d …
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11
votes
Vopěnka's Principle for non-first-order logics
Since the title of your question is, "Vopenka's Principle for non-first-order logics", this, from Magidor's and Vaananen's paper "On Lowenheim-Skolem-Tarski numbers for extensions of first order logic …
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2
votes
0
answers
676
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Boolean-Valued Models vs. the Infinite-valued Logic of Lukasiewicz and set theory
Is anyone familiar with an old paper of C.C. Chang entitled "The Axiom of Comprehension in Infinite-Valued Logic" which shows that the Axiom of Comprehension without parameters is consistent in the in …
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