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Results tagged with lo.logic
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user 4753
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.
6
votes
1
answer
268
views
$\omega_2$-sequence of Suslin trees
Is it possible to have an $\omega_2$-length sequence of ($\omega_1$-)Suslin trees such that if one builds the product of finitely many trees in that sequence, one ends up with a Suslin tree again?
Th …
- 2,381
8
votes
What ccc forcings add a Suslin tree?
It is consistent that the answer is no.
If we start with $L$ as our ground model then whenever $T$ is a Suslin tree, the forcing $\mathbb{P}_T$ which shoots a branch through $T$ will always introduce …
- 2,180
8
votes
The origins of forcing in mathematical logic and other branches of mathematics
One application I know is Scott's construction of forcing extensions of models of higher order theories of the Real numbers. Scott quickly after the invention of forcing, used a forcing argument to sh …
- 2,180
3
votes
Formal proof of Con(ZFC) => Con(ZFC + not CH) in ZFC
The usual strategy to prove that the negation of $CH$ is consistent with $ZFC$ is the following: One shows (under the assumption $Con(ZFC)$ that for any finite fragment $T$ of $ZFC$ we have that $T+ …
- 2,180
3
votes
3
answers
448
views
Complexity of the statement 'P is proper'
Assume that $(P,\le)$ is a notion of forcing. There are several ways to define what it means for $P$ being proper and I would like to know: What is the complexity (in terms of the Levy-Hierarchy) of t …
- 3,982
3
votes
Complexity of the statement 'P is proper'
I think that I might have found a solution to this rather dispensable question. I will sketch it:
Consider the following characterization of properness:
$P$ is proper iff for all $\lambda > 2^{|P|}$ …
- 2,180
3
votes
1
answer
583
views
Equivalent definitions of $(M,P)$-genericity
Hi!
I started to read the chapter 31 in Jechs book about proper forcing. Unfortunately it is written in a rather sketchy way and I do have some issues in proving a lemma about two equivalent definiti …
- 3,982
5
votes
1
answer
556
views
Why is this set stationary?
Hi
I really need a proof for the following statement by Baumgartner:
There exists a stationary subset of $[\omega_2]^{\omega}$ of size $\aleph_2$.
This is Exercise 38.15. in Jechs Book (2003) and …
- 24.8k
23
votes
Set theory and Model Theory
I totally agree with the answers already given but I still want to say something to your question, which emphasizes probably the formalist side. To cut a long story short the foundation of model theor …
- 2,180