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Ross Brady. Universal logic. CSLI Lecture Notes, vol. 109. CSLI Publications, Stanford, 2006, xii + 346 pp.

Published online by Cambridge University Press:  15 January 2014

Greg Restall
Greg Restall*
Affiliation:
School of Philosophy, University of Melbourne, Australia. restall@unimelb.edu.au.
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Type
Reviews
Information
Bulletin of Symbolic Logic , Volume 13 , Issue 4 , December 2007 , pp. 544 - 547
Copyright
Copyright © Association for Symbolic Logic 2007

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References

1 For (GCA), we define the status of a ∈ {xy: ϕ(x, y)} at α in terms of ϕ(a,{xy: ϕ(x, y)}). This is no trouble than the case for (CA).

2 The fixed point for negation is the statement r ∈ r, where r is {x: x ∉ x}, since we have r ∈ r ↔ ¬(r ∈ r). This generalises to any propositional function: we have {x: F(x ∈ x)} ∈ {x: F(x ∈ x)} ↔ F({x: F(x ∈ x)} ∈ {x: F(x ∈ x)}) for any propositional function F.