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page 39 should have been page 38--incorrect reference
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Thomas Benjamin
Thomas Benjamin
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In his book On Numbers and Games (pg. 3938) John Horton Conway makes the following remark, "But the collection of all gaps is not even a Proper Class, being an illegal object in most set theories." Is it true that the collection of all gaps is an "illegal object" in most set theories, and in what set theories is this collection not an illegal object? Conway's system No seems to handle gaps quite nicely, even without an axiomatization of set theory.

In his book On Numbers and Games (pg. 39) John Horton Conway makes the following remark, "But the collection of all gaps is not even a Proper Class, being an illegal object in most set theories." Is it true that the collection of all gaps is an "illegal object" in most set theories, and in what set theories is this collection not an illegal object? Conway's system No seems to handle gaps quite nicely, even without an axiomatization of set theory.

In his book On Numbers and Games (pg. 38) John Horton Conway makes the following remark, "But the collection of all gaps is not even a Proper Class, being an illegal object in most set theories." Is it true that the collection of all gaps is an "illegal object" in most set theories, and in what set theories is this collection not an illegal object? Conway's system No seems to handle gaps quite nicely, even without an axiomatization of set theory.

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Thomas Benjamin
Thomas Benjamin
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  • 39

A question regarding a remark of John Horton Conway

In his book On Numbers and Games (pg. 39) John Horton Conway makes the following remark, "But the collection of all gaps is not even a Proper Class, being an illegal object in most set theories." Is it true that the collection of all gaps is an "illegal object" in most set theories, and in what set theories is this collection not an illegal object? Conway's system No seems to handle gaps quite nicely, even without an axiomatization of set theory.