Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

300 indexthe Areopagite (Dionysius), 31–34, 41tArian heresies/Arius/Arianism, 28, 261, 265,278Aristotleon actual infinity, 23and the apeiron, 9, 21, 21n7and Aquinas, 291and Archimedes, 58–60the Archytas argument in, 170categorical methodology of, 35and Dante, 170–71eadem est scientia oppositorum concept of,292and Eunomius, 28finitist approach of, 22–23, 64, 73geocentrism in, 38and infinite sets, 183on infinite space, 22infinity as a property of God in, 23, 42infinity as negative in, 277–78infinity as positive in, 278n9on limits and bounds, 235metaphysics of form, 258ontology in, 258and Origenes, 27physics and the infinite in, 167on potential infinity, 9, 21–24, 32, 35, 39, 41t,76, 183n4, 256–58, 268, 278on prime matter, 256rational methodology of, 21–22, 33–34thinking of the infinite in, 174on time and motion as infinite, 22–23, 38transcendence in, 268Artin’s conjecture, 70atoms of space, 168Augustine, Saint, 27–28, 27n59, 36, 211, 260,263, 265–66, 278axiom of choice (AC)axioms implying, 92axioms refuting, 95, 99–101, 114, 117and the continuum hypothesis, 281n19forced failure of, 102–3, 106and God, 235n2and the HOD class, 101–2identified, 91in Kunen’s proof, 99necessity of, 95–96and regular cardinals, 116Russell’s illustration of, 77–78in theology, 251and transfinite cardinals, 2and the universe of sets, 100and Z set theories, 66–67, 77–78, 100, 132Axiom of Constructibility, 112Axiom of Determinacy (AD), 95–96axiom of infinity, 91, 134, 139axioms of P, 78, 83Ax-Kochen theorem, 70B (Basic axiom). See Basic axiomBaire sets, 108–9Banach-Tarski paradox, 67. SeealsoTarski,AlfredBarth, Karl, 42, 270baryons, 187, 198–99, 199n14Basic axiom (B), 131–32, 137–40, 143, 145–48,150–56, 158–64b-boundary, 222–24being. See en; theOneBerkeley, George, 62Bersanelli, Marco, 5–7, 12, 14–15, 193–214better than (system), 4, 130–31, 137–39, 163.See also much better than (MBT) systemBig Bangas cosmological model, 177–78and FLRW, 177and infinite time, 6and infinity, 7and inflationary cosmology, 178–80, 185,196vs. Judeo-Christian traditions, 211singularities in, 219–20universality of, 225Big Crunch singularity, 220Boethius, Anicius Manilus, 36, 227, 286n25,287Boltzmann, Ludwig, 200Boltzmann brain paradox, 188, 200–201Bolzano, Bernard, 13, 38–39, 39n106, 42n112,65, 279Bombieri, Enrico, 2, 9, 55–74Bondi, Hermann, 178, 200n17Bosshardt, B., 222Brouwer, Luitzen, 66, 81bubble models, 7, 179–88, 179f, 181f, 182f,186fBurali-Forti paradox, 66, 282–83n22Buridan, John, 32busy beaver problem, 71–74Cantor, Georg. See also the Absolute; alephs;continuum hypothesis; infinite sets;reflection principle; Russell, Robert John;the transfinite; transfinite numbers;transfinite setson Absolute Infinity, 1, 9–10, 40–41, 41n108,193n1, 248n9, 282–85, 287, 294on actual infinity, 1, 4, 9, 25, 38–42