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

index 305indeterminacy, 12, 255–57, 259, 273–74,290–91, 297indiscernibility principle, 226individualization principle, 226inductionin Lemma arithmetic, 149, 155, 161ordinals defined by, 89, 100and P, 134and Peano arithmetic, 81–83theorems proved by, 78transfinite, 38, 47, 61, 97, 144infinite cardinal numbers, 66, 248–49infinite divisibility of space, 167–70infinite extension of physical space, 167, 170–72infinitely distant/divergent singularities, 7–8,219–21, 224, 226–27, 234infinite setsand Aristotle, 183arithmetic rules for, 38n102bigger vs. smaller in, 37–39Cantor on, 38n102the common vs. the rare in, 200contradictions in, 77and finite sets, 279–82Galileo on, 279Gödel on, 14, 38and infinity, 39–40, 178mathematics applied to, 280–82as objectively existing objects, 14in the realm of the infinite, 100, 103–4real numbers in, 226reflection principle in, 14and repetition, 6, 11of states, 190as transfinite cardinals, 2and ZF axiom six, 67ZF theory of, 2infinite space. Seealsoinfinite divisibility ofspace; physical universeAristotle on, 22center absent from, 195vs. finite space, 6–7, 194–95inaccessibility of, 6, 190, 196, 219infinite replication in, 225–26and infinite time, 183mathematical models of, 76–78Nicholas of Cusa on, 38and physical infinity, 194–96and physical space, 5–8, 170–72questions regarding, 218as structureless, 195infinite time, 6–7, 61, 120, 176, 183, 219infinite time of inflation, 180–82, 181f, 185–86,186f“Infinities and the Nostalgia of the Stars”(Bersanelli), 193–214“Infinities in Cosmology” (Heller), 218–28infinities of the small, 8, 167–74, 177, 196n10infinity as a metaphysical concept, 255–57“Infinity as a Transformative Concept inScience and Technology” (Achtner), 19–47infinity as negative, 13, 32, 55, 234, 255,277–78, 283, 291, 295–98infinity as positive, 9, 12, 21, 267, 269–72, 278,278n9, 298infinity contexts, 1–15infinity definitions, 233–34infinity in physics overview, 167–75infinity of universes, 224–26inflationary cosmology, 7, 178–90, 179f, 181f,182f, 186f, 196, 198, 225inflationary multiverse, 184–88, 190–91,196Inner Model Program (Woodin), 3, 112–14,116–17intelligent design, 225, 228, 251n10Interpretation Hierarchy, 137interpretation power in concept calculus,132–37isotropic space/spacetimes. See homogeneousand isotropic space/spacetimesJewish religious traditions, 23, 211–13, 211–14,260.SeealsoPhilo of AlexandriaJohn of Damascus, 31, 31n69, 33John of the Cross, Saint, 226Judeo-Christian tradition, 194, 210–14. SeealsoChristian theologyKaku, Michio, 8Kant, Immanuel, 39, 43–44, 272, 291Kaye, Richard, 134Kierkegaard, Søren, 42, 43n114, 45–46, 46fKronecker, Leopold, 280Kronheimer, E. H., 223Kunen, Kenneth, 98–99large cardinal axioms, 3, 67, 91, 97–104, 106,110–17, 163last scattering surface, 196Leibniz, Gottfried Wilhelm, 39, 58, 62, 226,274, 279Lemma mathematics, 143–63Leopardi, Giacomo, 206, 208–9Lessing, Gotthold Ephriam, 59Lewis, A. C., 45n125, 235n2lightlike geodesics/infinities, 219–22light speed, 7, 178, 180–83, 182f, 196