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Title of Journal: Arch Math Logic

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Abbravation: Archive for Mathematical Logic

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Springer Berlin Heidelberg

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DOI

10.1007/978-3-642-35728-2_15

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1432-0665

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Maximally embeddable components

Authors: Miloš S Kurilić
Publish Date: 2013/06/06
Volume: 52, Issue: 7-8, Pages: 793-808
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Abstract

We investigate the partial orderings of the form langle mathbbPmathbbX subset rangle where mathbbX =langle X rho rangle is a countable binary relational structure and mathbbP mathbbX the set of the domains of its isomorphic substructures and show that if the components of mathbbX are maximally embeddable and satisfy an additional condition related to connectivity then the poset langle mathbbP mathbbX subset rangle is forcing equivalent to a finite power of Pω/ Fin+ or to the poset Pω × ω/Fin × Fin+ or to the product PDelta /fancyscriptEfancyscriptD rm fin+ times Pomega /rm Fin+n for some n in omega In particular we obtain forcing equivalents of the posets of copies of countable equivalence relations disconnected ultrahomogeneous graphs and some partial orderings

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  1. Homogeneous iteration and measure one covering relative to HOD
  2. On the indestructibility aspects of identity crisis
  3. Strict core fuzzy logics and quasi-witnessed models
  4. The large cardinals between supercompact and almost-huge
  5. Prefix and plain Kolmogorov complexity characterizations of 2-randomness: simple proofs
  6. A blend of methods of recursion theory and topology: A Π 1 0 tree of shadow points
  7. C-Quasi-Minimal enumeration degrees below c'
  8. The logic of equilibrium and abelian lattice ordered groups
  9. Register computations on ordinals
  10. On omega-categorical simple theories
  11. Some weak fragments of Martin’s axiom related to the rectangle refining property
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