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Results tagged with model-theory
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user 479330
Model theory is the branch of mathematical logic which deals with the connection between a formal language and its interpretations, or models.
1
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Is there a metamathematical $V$?
This may be more in line with Vincent R.B. Blazy's answer, but one thing I would like to add is the principle of inexhaustibility. This principle appears in Maddy's "Believing the Axioms. I", where it …
- 2,031
1
vote
Accepted
Minimal models in strong set theories - pt. 2
Negative answer for the first question: $L$ satisfies KP+"there exists a stable ordinal" but $L_\sigma$ does not. This is r.e. because "there exists a stable ordinal" can be expressed by a single axio …
- 2,031
2
votes
0
answers
206
views
Some questions about the Hyperuniverse Program
The Hyperuniverse Program, founded by Sy D. Friedman, intends to produce new second-order axioms of set theory which appropriately formalize "the universe is maximal" in one of a few ways. A height-ma …
- 2,031
6
votes
Smallest ordinal modelling $\aleph_1$?
About well-definedness of $X_1$, "being a model of ZFC" is definable since ZFC is a recursive theory, so we could construct some $\Sigma_1^0$ predicate $\textrm{isZFCAxiom}(e)$ for $e$ a Godel-coding …
- 2,031
1
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How to solve this exercise about large countable ordinals?
This is a partial result, which is that there is an $(M,E)$ satisfying all but the end-extension requirement, in place of $M$ being an end-extension of $L_{\gamma_1}$, there is just an $X\subseteq M$ …
- 2,031
3
votes
Parameter-free effective cardinals
Edit Jul 25: These results may be strengthenable by using theorem 7.8 of chapter V of Admissible Sets and Structures instead of lemma 1, I may edit this post in the future with any resulting improveme …
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