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The foundations of Suslin logic

Published online by Cambridge University Press:  12 March 2014

Erik Ellentuck
Erik Ellentuck*
Affiliation:
Rutgers University, New Brunswick, New Jersey 08903
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Extract

Let L be a first order logic and the infinitary logic (as described in [K, p. 6] over L. Suslin logic is obtained from by adjoining new propositional operators and . Let f range over elements of ωω and n range over elements of ω. Seq is the set of all finite sequences of elements of ω. If θ: Seq → is a mapping into formulas of then and are formulas of LA . If is a structure in which we can interpret and h is an -assignment then we extend the notion of satisfaction from to by defining

where f ∣ n is the finite sequence consisting of the first n values of f. We assume that has ω symbols for relations, functions, constants, and ω1 variables. θ is valid if θ ⊧ [h] for every h and is valid if -valid for every . We address ourselves to the problem of finding syntactical rules (or nearly so) which characterize validity .

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 40 , Issue 4 , December 1975 , pp. 567 - 575
Copyright
Copyright © Association for Symbolic Logic 1975

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References

REFERENCES

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