# On certain maximality principles

Document Type: Research Paper

Author

Department of Mathematics and Computer Sciences‎, ‎Amirkabir University of Technology‎, ‎Hafez Avenue 15194‎, ‎Tehran‎, ‎Iran.

Abstract

‎We present streamlined proofs of certain maximality principles studied by Hamkins‎ ‎and Woodin‎. ‎Moreover‎, ‎we formulate an intermediate maximality principle‎, ‎which is‎ ‎shown here to be equiconsistent with the existence of a weakly compact cardinal $\kappa$ such that $V_{\kappa}\prec V$‎.

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Main Subjects

### References

J. Cummings, Iterated forcing and elementary embeddings, in: Handbook of Set Theory, Vols. 1, 2, 3, pp. 775--883, Springer, Dordrecht, 2010.

J.D. Hamkins, A simple maximality principle, J. Symbolic Logic 68 (2003), no. 2, 527--550.

J.D. Hamkins, W.H. Woodin, The necessary maximality principle for c.c.c. forcing is equiconsistent with a weakly compact cardinal, MLQ Math. Log. Q. 51 (2005), no. 5, 493--498.

L. Harrington, S. Shelah, Some exact equiconsistency results in set theory, Notre Dame J. Formal Logic 26 (1985), no. 2, 178--188.

### History

• Receive Date: 06 March 2016
• Revise Date: 17 May 2016
• Accept Date: 20 May 2016