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Fundamenta Mathematicae

1991-1992 | 140 | 2 | 137-155
Tytuł artykułu

Relatively recursive expansions

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we consider the following basic question. Let A be an L-structure and let ψ be an infinitary sentence in the language L∪{R}, where R is a new relation symbol. When is it the case that for every B ≅ A, there is a relation R such that (B,R) ⊨ ψ and $R ≤_T D(B)$? We succeed in giving necessary and sufficient conditions in the case where ψ is a "recursive" infinitary $Π_2$ sentence. (A recursive infinitary formula is an infinitary formula with recursive disjunctions and conjunctions.) We consider also some variants of the basic question, in which R is r.e., $Δ_α^0$, or $Σ_α$ instead of recursive relative to D(B).
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
137-155
Opis fizyczny
Daty
wydano
1992
otrzymano
1990-09-18
poprawiono
1991-09-19
Twórcy
autor
• Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia, Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, U.S.A.
autor
• Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia, Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, U.S.A.
Bibliografia
• [A1] C. J. Ash, Recursive labelling systems and stability of recursive structures in hyperarithmetic degrees, Trans. Amer. Math. Soc. 298 (1986), 497-514; Correction, ibid. 310 (1988), 851.
• [A2] C. J. Ash, Labelling systems and r.e. structures, Ann. Pure Appl. Logic 47 (1990), 99-119.
• [AC] C. J. Ash and J. Chisholm, Notions of relatively recursive categoricity, in preparation.
• [AKMS] C. J. Ash, J. F. Knight, M. Manasse and T. Slaman, Generic copies of countable structures, Ann. Pure Appl. Logic 42 (1989), 195-205.
• [AN] C. J. Ash and A. Nerode, Intrinsically recursive relations, in: Aspects of Effective Algebra, J. N. Crossley (ed.), U.D.A. Book Co., Yarra Glen, Australia, 1981, 26-41.
• [C] J. Chisholm, Effective model theory vs. recursive model theory, J. Symbolic Logic 55 (1990), 1168-1191.
• [K] J. F. Knight, Degrees coded in jumps of orderings, ibid. 51 (1986), 1034-1042.
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