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Results tagged with lo.logic
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user 38966
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
Ultraproduct of Dividing Lines
I think, in general, it would be hard to say somethings about $T$. For example, finite linear orders satisfy stability (and hence simplicity). However a non principal ultraproduct of finite linear ord …
- 1,872
8
votes
1
answer
641
views
Applications of "model-theoretic" forcing
The notion of forcing was invented by Paul Cohen, who used
it to prove the independence of the Continuum Hypothesis. He constructed a model of set theory in which the CH fails, thus showing that CH i …
- 1,872
3
votes
1
answer
388
views
The number of countable models [duplicate]
Let $\mathcal{L}$ be a countable first order language. For a natural number n, can we find a complete $\mathcal{L}$-Theory $T$ which has exactly n non-isomorphic countable models ?
- 1,872
4
votes
1
answer
363
views
Uncountably categorical theories which are interpretable in a strongly minimal
Definition: Let $\lambda$ be a cardinal. An $\mathcal{L}$-theory $T$ is called $\lambda$-categorical whenever every two models of $T$ of cardinality $\lambda$ are isomorphic.
Definition: An $\mathc …
- 1,872
3
votes
1
answer
160
views
Strongly minimal set with DMP
Recall that a strongly minimal theory $T$ has the Definable Multiplicity Property (DMP) if for all natural $k$, $m$ and $\varphi(\bar{x},\bar{b})$ of rank $k$, multiplicity $m$, there exists a formula …
- 1,872
6
votes
2
answers
306
views
The role of the index set in the product of uncountably many topological spaces
Let $\langle X_i,\mathcal{T}_i \rangle_{i\in I}$ be a family of topological spaces. Consider $X=\prod_{i\in I} X_i$ with product topology.
Question. Is there a topological property that holds in …
- 1,872
6
votes
0
answers
261
views
Stability of analytic Zariski structures
Noetherian Zariski structures are introduced by Hrushovski and Zilber(1996).
An analytic Zariski structure is a generalization of Noetherian Zariski structures, introduced by Zilber and Peatfield.
Fo …
- 1,872
7
votes
1
answer
438
views
Groups and pregeometries
Definition.
For an infinite structure $\mathcal{A}$ and $cl : P(dom(\mathcal{A})) \longrightarrow P(dom(\mathcal{A}))$ , we say
that $(\mathcal{A}, cl)$ is a structure carrying an $\omega$-homogeneous …
- 1,872
12
votes
0
answers
1k
views
Hrushovski's Construction
Zilber expressed a conjecture for $\aleph_{1}$- categorical theories (In the 80s).
Zilber's Conjecture: The geometry of any $\aleph_{1}$- categorical structure is one of the following:
(a) Trivial ( …
- 1,872
16
votes
6
answers
2k
views
Application of Fraïssé construction in set theory
As you know Fraïssé limit construction and its generalization, Hrushovski's construction, have many applications in model theory to build models with interesting property.
Now I would like to know th …
- 1,872