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comment Is the theory of real closed fields expanded by restricted analytic functions decidable?
Isn't the language uncountable here? If so than you can't encode formulas by numbers, so there is no notion of decidability.
Aug
21
reviewed Reject Prove that a Cauchy sequence of piecewise functions does not converge unde the $L_1$ norm.
Aug
21
reviewed Approve Locally Compact Group with Haar Measure
Aug
21
reviewed Approve Graph Path Length Problem
Aug
21
answered Doubt about the proof on uniqueness of saturated model
Aug
20
comment Why are algebras classified as being of a certain type?
I think $o(\tau)$ is the number of operations and $n_\gamma$ is the arity of the operation $\mathbf f_\gamma$. In other words $\gamma < o(\tau)$ does not limit any arity.
Jul
18
answered number of types if isolated types are dense
Jul
2
awarded  Enlightened
Jul
2
awarded  Nice Answer
Jul
2
comment Non-standard model of $Th(\mathbb{R})$ with the same cardinality of $\mathbb{R}$
Let $f : ^{\star}\mathfrak R \to \mathfrak R$ be a bijection. Then for some natural number $n$, we have $1 + 1 + ... +1 > f(c)$, whereas $1 + 1 + ... +1 < c$ (the addition is $n$-times). Thus $f$ does not preserve formulas.
Jun
4
awarded  Yearling
May
28
comment Generalizations of pregeometries
I don't think your theory is uncountably categorical. One can vary the sizes of equivalence classes and obtain many models.
May
25
comment Functions or relations stable under automorphism
Your claim that invariant subsets in a saturated model are definable is not correct. Say any type definable set is invariant under automorphisms fixing its base.
May
9
comment Characterization of superstability
I am not aware of any such characterisation, I don't think you can do much better than finite.
May
8
answered Characterization of superstability
Apr
26
comment Morley’s Categoricity Theorem for uncountable languages.
Accessible expositions of Shelah's work are hard to find. I personally haven't seen any exposition of Morley's theorem for uncountable languages not by Shelah.
Apr
22
comment Show For any language L two L-structures M and N are elementarily equivalent iff they are elementarily equivalent for every finite sublanguage.
Suppose $\mathcal M \not \equiv \mathcal N$. Then there is a formula $\phi$ such that $\mathcal M \models \phi$ and $\mathcal N \models \lnot \phi$. Now use the hint.
Apr
21
answered Show For any language L two L-structures M and N are elementarily equivalent iff they are elementarily equivalent for every finite sublanguage.
Apr
16
awarded  Custodian
Apr
16
reviewed Approve Are there arbitratily long runs of consecutive integers n that are NOT of the form $n = p^k$ or $n = 2p^k$ for some $k>0$ and $p$ an odd prime?