Realizing and Omitting Types

Marker, D. (2002). Realizing and Omitting Types: An Introduction. Model Theory: An Introduction.

Type

Book

Intellectual base

Review or monograph

Year

2002

DOI

10.1007/b98860

ISBN

9780387987606

DOI registrant

Springer Nature

Link

https://doi.org/10.1007/b98860

Cited from

mathematics

Cited by

7 citations across 7 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Local-to-Global Aggregation
  • Logic (compactness) — a set of first-order sentences is satisfiable iff every finite subset is; local finite-subset satisfiability aggregates to global satisfiability.

    This sourceStates and proves the compactness theorem: a set of first-order sentences is satisfiable iff every finite subset is, with an unsatisfiable finite fragment localizing any inconsistency.

Domain-specific

• Back-and-Forth Method
  • It recurs in proofs for countable dense linear orders without endpoints, the countable random graph, countable atomless Boolean algebras, homogeneous structures, and model-theoretic equivalence criteria.
• Definable set
  • A definable set turns logical syntax into a semantic subset of a structure.
• Diagram (mathematical logic)
  • … and a convenient observable transfers from A canonical example satisfies the full defining rule of Diagram (mathematical logic) with assumptions and conventions explicit. to A careful use of Diagram (mathematical logic) tests the constitutive rule and nearest confusable rather than relying on the label alone..
• Indiscernibles
  • Marker develops this definition, its Ramsey-theoretic existence tools, and Ehrenfeucht–Mostowski applications as a unified chapter of model construction.
• Prime Model (Model Theory)
  • Thus the image preserves the entire first-order structure, not merely operations or relations.
• Reduct
  • They let theorems be transferred downward when they mention only retained symbols, and expose which properties depend on enriched vocabulary.

Verification

Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.

Does it back the claim? Not recorded. Neither this nor any other of the 7 citations of this work carries a recorded support check.

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Links previously used in the corpus

Before the registry existed this work was also linked 1 other way.

• https://homepages.math.uic.edu/~marker/mtcont.html ×1

Registry ID ref:47f091c375ce · see in the full table