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Flash Sheridan
Flash Sheridan
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Have a look at Church’s (first) Set Theory with a Universal Set, which is equiconsistent with ZFGC, though Church didn’t publish a full proof, and I think he abandoned the proof in his archives at Princeton. (My forthcoming doctoral thesis completes the proof for a variant with the singleton function as a set.) His archives also contain lecture notes on some more complicated theories with approximately the same name, but I believe he gave up on those theories, not just the details of the consistency proofs.

• Alonzo Church (1974). “Set Theory with a Universal Set,” Proceedings of the Tarski Symposium. Proceedings of Symposia in Pure Mathematics XXV,Proceedings of the Tarski Symposium. Proceedings of Symposia in Pure Mathematics XXV, ed. L. Henkin, American Mathematical Society, pp. 297–308.

• T. E. Forster (1995). Set Theory with a Universal Set: Exploring an Untyped UniverseSet Theory with a Universal Set: Exploring an Untyped Universe (Oxford Logic Guides 31). Oxford University Press. ISBN 0-19-851477-8.

• T. E. Forster (2001). “Church’s Set Theory with a Universal Set.”

See also the Wikipedia article (disclaimer: I started it in its current form.)

Have a look at Church’s (first) Set Theory with a Universal Set, which is equiconsistent with ZFGC, though Church didn’t publish a full proof, and I think he abandoned the proof in his archives at Princeton. (My forthcoming doctoral thesis completes the proof for a variant with the singleton function as a set.) His archives also contain lecture notes on some more complicated theories with approximately the same name, but I believe he gave up on those theories, not just the details of the consistency proofs.

• Alonzo Church (1974). “Set Theory with a Universal Set,” Proceedings of the Tarski Symposium. Proceedings of Symposia in Pure Mathematics XXV, ed. L. Henkin, American Mathematical Society, pp. 297–308.

• T. E. Forster (1995). Set Theory with a Universal Set: Exploring an Untyped Universe (Oxford Logic Guides 31). Oxford University Press. ISBN 0-19-851477-8.

• T. E. Forster (2001). “Church’s Set Theory with a Universal Set.”

See also the Wikipedia article (disclaimer: I started it in its current form.)

Have a look at Church’s (first) Set Theory with a Universal Set, which is equiconsistent with ZFGC, though Church didn’t publish a full proof, and I think he abandoned the proof in his archives at Princeton. (My forthcoming doctoral thesis completes the proof for a variant with the singleton function as a set.) His archives also contain lecture notes on some more complicated theories with approximately the same name, but I believe he gave up on those theories, not just the details of the consistency proofs.

• Alonzo Church (1974). “Set Theory with a Universal Set,” Proceedings of the Tarski Symposium. Proceedings of Symposia in Pure Mathematics XXV, ed. L. Henkin, American Mathematical Society, pp. 297–308.

• T. E. Forster (1995). Set Theory with a Universal Set: Exploring an Untyped Universe (Oxford Logic Guides 31). Oxford University Press. ISBN 0-19-851477-8.

• T. E. Forster (2001). “Church’s Set Theory with a Universal Set.”

See also the Wikipedia article (disclaimer: I started it in its current form.)

Source Link
Flash Sheridan
Flash Sheridan
  • 723
  • 9
  • 7

Have a look at Church’s (first) Set Theory with a Universal Set, which is equiconsistent with ZFGC, though Church didn’t publish a full proof, and I think he abandoned the proof in his archives at Princeton. (My forthcoming doctoral thesis completes the proof for a variant with the singleton function as a set.) His archives also contain lecture notes on some more complicated theories with approximately the same name, but I believe he gave up on those theories, not just the details of the consistency proofs.

• Alonzo Church (1974). “Set Theory with a Universal Set,” Proceedings of the Tarski Symposium. Proceedings of Symposia in Pure Mathematics XXV, ed. L. Henkin, American Mathematical Society, pp. 297–308.

• T. E. Forster (1995). Set Theory with a Universal Set: Exploring an Untyped Universe (Oxford Logic Guides 31). Oxford University Press. ISBN 0-19-851477-8.

• T. E. Forster (2001). “Church’s Set Theory with a Universal Set.”

See also the Wikipedia article (disclaimer: I started it in its current form.)