A Survey of Mathematical Logic

A Survey of Mathematical Logic

A Survey of Mathematical Logic

A Survey of Mathematical Logic

Excerpt

Some time ago it was suggested that a collection of my papers in the field of mathematical logic be put forth. As the papers deal with only a few subdomains of the field, I have added from unpublished notes discussions of a number of standard topics and replaced a few papers by somewhat more general descriptions of related matter. The result is the present book.

As a survey, it is neither complete nor impartial. For example, modal logic, combinatory logic, and many-valued logic are not considered at all. More serious omissions are any adequate account of more recent works on recursive functions and on intuitionism, two of the subjects which are of the greatest current interest among working mathematical logicians. But these two fields are in the midst of rapid developments; there seems to be no choice but to follow new discoveries as they come out. In a different direction, works not easily accessible to me have not been adequately dealt with.

For the material contained in the present book, I am heavily indebted to various persons for discussions, suggestions, and criticisms. On matters having to do with axiomatic set theory and metamathematics, my indebtedness is chiefly to Bernys, Kreisel, McNaughton,, Quine, Rosser, and Specker; in the area of calculating machines, to A. W. Burks, B. Dunham, E. F. Moore, G. W. Patterson, and J. C. Shepherdson. In my earlier education, Chin Yueh-Lin, Shen Yu-Ting, and especially Wang Hsien-Chun have selflessly taught me mathematical logic. In more recent years, Hu Shih-Hua has given me much encouragement.

HAO WANG

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