This English translation of the author's original work has been
thoroughly revised, expanded and updated.
The book covers logical systems known as "type-free" or
"self-referential." These traditionally arise from any discussion
on logical and semantical paradoxes. This particular volume,
however, is not concerned with paradoxes but with the investigation
of type-free sytems to show that: (i) there are rich theories of
self-application, involving both operations and truth which can
serve as foundations for property theory and formal semantics; (ii)
these theories provide a new outlook on classical topics, such as
inductive definitions and predicative mathematics; (iii) they are
particularly promising with regard to applications.
Research arising from paradoxes has moved progressively closer
to the mainstream of mathematical logic and has become much more
prominent in the last twenty years. A number of significant
developments, techniques and results have been discovered.
Academics, students and researchers will find that the book
contains a thorough overview of all relevant research in this
field.
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