In this paper, we are concerned with the arithmetical definability of certain notions of integers and rationals in terms of other notions. The results derived will be applied to obtain a negative solution of corresponding decision problems.In Section 1, we show that addition of positive integers can be defined arithmetically in terms of multiplication and the unary operation of successorS(whereSa=a+ 1). Also, it is shown that both addition and multiplication can be defined arithmetically in terms of successor and the relation (...) of divisibility | (wherex|ymeansxdividesy). (shrink)

In the vast literature on architectural theory and practice, the ways in which architectural knowledge is actually taught, debated, and understood are too often ignored. The essays collected in this groundbreaking volume address the current state of architecture as an academic and professional discipline. The issues considered range from the form and content of architectural education to the architect's social and environmental obligations and the emergence of a new generation of architects. Often critical of the current paradigm, these essays offer (...) a provocative challenge to accepted assumptions about the production, dissemination, and reception of architectural knowledge. Contributors: Sherry Ahrentzen, U of Wisconsin-Milwaukee; Stanford Anderson, MIT; Carol Burns, Harvard U; Russell Ellis, UC Berkeley; Thomas Fisher, U of Minnesota; Linda Groat, U of Michigan; Kay Bea Jones, Ohio State U; David Leatherbarrow, U of Pennsylvania; A. G. Krishna Menon, TVB School of Habitat Studies, India; Garth Rockcastle, U of Minnesota; Michael Stanton, American U, Beirut; Sharon E. Sutton, U of Washington; David J. T. Vanderburgh, Université Catholique de Louvain, Belgium; and Donald Watson, Rensselaer Polytechnic Institute. (shrink)