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bio website www1.maths.leeds.ac.uk/~mmdt
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visits member for 2 years, 8 months
seen 17 hours ago

2010 - 2014, Imperial College London, MEng Computing (Artificial Intelligence)

2014 - 2017, University of Leeds, a PhD candidate in Computability Theory


Jan
26
accepted No generic is definable in a perfect notion of forcing of a model of Peano Arithmetic
Jan
26
revised No generic is definable in a perfect notion of forcing of a model of Peano Arithmetic
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Jan
26
asked No generic is definable in a perfect notion of forcing of a model of Peano Arithmetic
Jan
23
accepted Are there elementarily equivalent models $\mathcal{M}, \mathcal{N}$ of the same cardinality s.t. neither can be elementarily embedded into the other?
Jan
23
comment Are there elementarily equivalent models $\mathcal{M}, \mathcal{N}$ of the same cardinality s.t. neither can be elementarily embedded into the other?
I do not understand how you can apply back-and-forth property: let $h:\mathcal{M} \rightharpoonup \mathcal{N}$ be a finite partial isomorphism between your first and the second model. Then there exists $a_N \in L$ such that $a_N^{\mathcal{M}}>1$ and $a_N^{\mathcal{N}}<1$ so you cannot extend $h$ by $a_N^{\mathcal{M}}$ as any such extended bijection would not preserve the interpretation of the constant $a_N$ and hence would not be an isomorphism.
Jan
21
comment What is an omega model?
Let us continue this discussion in chat.
Jan
21
comment What is an omega model?
@AsafKaragila Thank you. Unless somebody else posts another definition, I would like to accept your comment as an answer.
Jan
21
comment What is an omega model?
If an omega model is not a general terminology and I cannot provide the context, perhaps I should delete the question.
Jan
21
comment What is an omega model?
@AsafKaragila They may have meant some theory of graphs meeting certain specific properties - e.g. it has to be directed, have a root, be a subgraph of some specific graph, etc. But the question was quite out of the context of the main talk, that is why I thought, the terminology may have a general meaning. But if you do not know, then it probably is not an established terminology.
Jan
21
asked What is an omega model?
Jan
20
comment Motivation behind automorphism bases?
@PrimoPetri Is there anything more one can use the automorphism bases when inspecting the automorphism group of the Turing degrees (en.wikipedia.org/wiki/Turing_degree) in particular? Even if you could direct me to too broad or general sources of which you know, I would find that helpful.
Jan
19
comment Formula for automorphism between sequence of real numbers
In your suggestion to the solution, 4 gets send to 8 only, it is 2 that gets sent to 4 (not 4 to 2). So you could still establish a bijection.
Jan
18
revised Are there elementarily equivalent models $\mathcal{M}, \mathcal{N}$ of the same cardinality s.t. neither can be elementarily embedded into the other?
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Jan
18
revised Are there elementarily equivalent models $\mathcal{M}, \mathcal{N}$ of the same cardinality s.t. neither can be elementarily embedded into the other?
deleted 2 characters in body; edited title
Jan
18
revised Are there elementarily equivalent models $\mathcal{M}, \mathcal{N}$ of the same cardinality s.t. neither can be elementarily embedded into the other?
deleted 2 characters in body; edited title
Jan
18
asked Are there elementarily equivalent models $\mathcal{M}, \mathcal{N}$ of the same cardinality s.t. neither can be elementarily embedded into the other?
Jan
1
accepted Is there an incomplete Turing degree that is not r.e.?
Jan
1
revised Is there an incomplete Turing degree that is not r.e.?
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Dec
31
asked Is there an incomplete Turing degree that is not r.e.?
Dec
30
comment Diagonalization
It is hard to answer your question as you have not defined a diagonalization formally. But most of the results about the existence of some classes of sets (degrees) are proved with the priority methods which do not use an explicit diagonalization and it would be hard to imagine to prove such results with the diagonalization techniques alone. C.f. Friedberg-Muchnik theorem, www1.maths.leeds.ac.uk/~pmt6sbc/3163/FMslides.pdf.