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Results tagged with lo.logic
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user 11115
first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
7
votes
1
answer
326
views
Effective set= ordinal definable set
I just today realized that the concept of ordinal definability is defined in a different way by vopenka-Balcar-Hajek ``The notion of effective sets and a new proof of the consistency
of the axiom of …
- 32.2k
8
votes
0
answers
182
views
Topological Vaught's conjecture for special theories
As is know, Vaught's conjecture is a special case of topological Vaught's conjecture.
On the other hand, the Vaught's conjecture is true for the following theories:
1- $\omega$-stable theories (Shel …
- 32.2k
14
votes
1
answer
414
views
Definability in the field of reals with a predicate for some powers of two
In "The field of reals with a predicate for the powers of two", Van den Dries has proved that the set of integers is not definable in $(\mathbb{R}, +,\cdot, \leq, 0, 1, 2^{\mathbb{Z}})$, where
$2^{ …
- 32.2k
5
votes
0
answers
191
views
Product of nice proper forcing notions
Question Are there forcing notions $P$ and $Q$ such that $P$ is proper and $\aleph_2$-cc, $Q$ is proper and satisfies the $\aleph_2$-pic (pic=properness isomorphism condition) such that $P \times Q$ i …
- 32.2k
3
votes
0
answers
175
views
Non-special $\aleph_2$-Aronszajn trees in the Laver-Shelah model for $\aleph_2$-Souslin hypo...
Assume $V=L$ and let $\kappa$ be a weakly compact cardinal. Let $G$ be $Col(\aleph_1, < \kappa)$ generic over $V$. Working in $V[G]$ force with a countable support iteration of forcing notions of leng …
- 32.2k
11
votes
2
answers
705
views
ZFC applications of Shelah's creature forcing
Shelah's creature forcing is a very powerful method, with wide range of applications. The method also has some applications in ZFC, let's quote a few of them that I am aware of:
(1) In A partition the …
- 32.2k
13
votes
0
answers
696
views
Applications of Set theory vs. model theory in mathematics
I have a question that has occupied my mind for some time.
Let's first consider applications of set theory and model theory in mathematics.
Major applications of set theory are in topology, Banach spa …
- 32.2k
5
votes
1
answer
663
views
Random real forcing
Let $\kappa$ be an infinite cardinal and let $B$ be the random forcing for adding $\kappa$-many random reals.
Question: What are the elements of $B$. More precisely given a condition $p \in B$, what …
- 32.2k
12
votes
2
answers
993
views
Kunen's inconsistency result
A well-known result of Kunen says that there is no non-trivial elementary embedding $j: V \rightarrow V.$ There are several proofs of this theorem (see Kanamori, The higher infinite). I wonder to know …
- 32.2k
6
votes
1
answer
294
views
Characterization of intermediate submodels of generic extensions
Question 1: Suppose that $V[G]$ is a set generic extension of $V$ by some forcing notion $P\in V,$ and suppose that $W$ is a model of $ZFC, V \subset W \subset V[G].$ Can we find a forcing notion $Q\i …
- 32.2k
12
votes
0
answers
372
views
Singular Jonsson cardinals
Is the following consistent?
$(*)$: There exists a singular cardinal $\kappa$ such that :
(1) $\kappa$ is a Jonsson cardinal,
(2) $\kappa$ is not a fixed point of the $\aleph-$function, i.e., $\kappa …
- 32.2k
7
votes
1
answer
258
views
Different ways of making $HOD$ far from $V$
There are different criteria for building a model $V$ of $ZFC$ which is far from its
$HOD$, for example:
$(A)$ Cardinality criteria: For this in a joint work with James Cummings and Sy Friedman, we …
- 32.2k
10
votes
0
answers
290
views
When does $HOD^{V[G]} \subseteq V$?
Assume that $\mathbb{P}\in HOD$ is non-trivial. It is well-known that if $\mathbb{P}$
satisfies some homogeneity properties, then $HOD^{V[G]} \subseteq V$, where $G$ is $\mathbb{P}$-generic over $V$.
…
- 32.2k
7
votes
1
answer
507
views
Non-homogeneous forcing and HOD
Is there a separative forcing notion $\mathbb{P}$ such that:
1) For any $p \in\mathbb{P}, \mathbb{P}/p = \{q \in \mathbb{P}: q \leq p \}$ is not forcing isomorphic to any homogeneous forcing notion, …
- 32.2k
10
votes
0
answers
273
views
Strongly compact vs Shelah cardinals
Does Con(ZFC+there exists a strongly compact cardinal) imply the Con(ZFC+there exists a Shelah cardinal)?
- 32.2k