Relatively recursive expansions

• Autorzy: C. J. Ash , J. F. Knight
• 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).

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1991-1992
• Tom: 140
• Numer: 2
• Strony: 137-155

Daty

wydano

1992

otrzymano

1990-09-18

poprawiono

1991-09-19

Twórcy

autor

C. J. Ash

• Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia, Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, U.S.A.

autor

J. F. Knight

• 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.