791 research outputs found
Canonical truth
No full textWe introduce and study some variants of a notion of canonical set theoretical truth. By this, we mean truth in a transitive proper class model M of ZFC that is uniquely characterized by some ∈-formula. We show that there are interesting statements that hold in all such models, but do not follow from ZFC, such as the ground model axiom and the nonexistence of measurable cardinals. We also study a related concept in which we only require M to be fixed up to elementary equivalence. We show that this theory-canonicity also goes beyond provability in ZFC, but it does not rule out measurable cardinals and it does not fix the size of the continuum
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Letter to Philippe-Antoine Merlin, 1802 November 12.
No full textLetter to Philippe-Antoine Merlin, concerning a conflict involving charges of plagarism between the author and C. Laucuouque, dated "21 brumaire, an 11." The author's signature is not entirely legible. Accompanying enveloped shows traces of red wax seal
On the value group of a model of Peano Arithmetic
No full textWe investigate IPA-real closed fields, that is, real closed fields which admit an integer part whose
non-negative cone is a model of Peano arithmetic. We show that the value group of an IPA-real closed field
is an exponential group in the residue field, and that the converse fails in general. As an application, we
classify (up to isomorphism) value groups of countable recursively saturated exponential real closed fields.
We exploit this characterization to construct countable exponential real closed fields which are not IPA-real
closed fields
Reachability for infinite time Turing machines with long tapes
No full textInfinite time Turing machine models with tape length α, denoted T_α, strengthen the machines of Hamkins and Kidder with tape length ω. A new phenomenon is that for some countable ordinals α, some cells cannot be halting positions of Tα given trivial input. The main open question in a paper of Rin from 2014 asks about the size of the least such ordinal δ. We answer this by providing various characterizations. For instance, δ is the least ordinal with any of the following properties: • For some ξ < α, there is a T_ξ-writable but not T_α-writable subset of ω. • There is a gap in the T_α-writable ordinals. • α is uncountable in L_(λ^α). Here λ^α denotes the supremum of Tα-writable ordinals, i.e. those with a T_α-writable code of length α. We further use the above characterizations, and an analogue to Welch’s submodel characterization of the ordinals λ, ζ and Σ, to show that δ is large in the sense that it is a closure point of the function α ﰁ→ Σ_α, where Σ_α denotes the supremum of the Tα-accidentally writable ordinals
Nurturing Biophilia: Merlin and Sanderling
No full textThe author develops a narrative of Merlin predation to illustrate the growth of biophilia. Initially descriptive, the story evolves by following an iterative process of questioning and relationship building, which leads to an informed and purposeful application of biophilia
Looking over Merlin Tanner's shoulder at team roping (GCCS_BCF231196_4_17)
No full textLooking over Merlin Tanner's shoulder at team roping during the Fourth of July rodeo. View is from the announcer's stand. July 6, 1985 in Grouse Creek, Utah. One black and white negative (1 x 2.25 inches)
Decision times of infinite computations
No full textThe decision time of an infinite time algorithm is the supremum of its halting times over all real inputs. The decision time of a set of reals is the least decision time of an algorithm that decides the set; semidecision times of semidecidable sets are defined similarly. It is not hard to see that ω 1 is the maximal decision time of sets of reals. Our main results determine the supremum of countable decision times as σ and that of countable semidecision times as τ, where σ and τ denote he suprema of Σ1and Σ2- definable ordinals, respectively, over Lω1. We further compute analogous suprema for singletons. <br/
The Beginning of Arthur and Merlin
No full textxiii, 34 p.The author explains the origin and literary inspiration for an original story of Arthur and Merlin for young readers
Entangled Lives: How Fungi Make Our Worlds, Change Our Minds, and Shape Our Futures
No full textMerlin Sheldrake, Biologist, speaker, and New York Times best-selling author. - Thinking about fungi makes the world look different. Most fungi live out of sight, yet make up a massively diverse kingdom of organisms that support and sustain nearly all living systems. Fungi throw our concepts of individuality and even intelligence into question. They can change our minds, heal our bodies, and help remediate environmental disaster. In this talk, Merlin will discuss the ways these extraordinary organisms – and our relationships with them – change our understanding of the planet on which we live, and the ways that we think, feel, and behave.https://scholarworks.boisestate.edu/ideas_of_nature_gallery/1041/thumbnail.jp
Merlin and Nimiane : the unifying force for the national unity of Britain at the waning of the Middle Ages as depicted by an anonymous author of the fifteenth-century "Prose Merlin"
No full textThe article analyses a special portrayal of the relationship between Merlin and Nimiane in the English fifteenth-century Prose Merlin. The power couple escapes from their previously distinct and usually dubious renditions to perform a new function that serves the nation-building of a reviving civilization. The political and religious inclinations of the anonymous author are visible in their almost impeccable conduct towards their sovereigns, God, and themselves. The article analyses the unique presentation of the two in the light of the political and social circumstances of the waning of the Middle Ages in Britain and contrasts them with a short analysis of other medieval portrayals of the couple
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