Real numbers and projective spaces : Intuitionistic reasoning with undecidable basic relations

Brouwer introduced in 1924 the notion of an apartness relation for real numbers, with the idea that whenever it holds, a finite computation verifies it in contrast to equality. The idea was followed in Heyting's axiomatization of intuitionistic projective geometry. Brouwer in turn worked out an intuitionistic theory of "virtual order." It is shown that Brouwer's proof of the equivalence of virtual and maximal order goes only in one direction, and that Heyting's axiomatization needs to be made a bit stronger. (C) 2018 Published by Elsevier B.V. on behalf of Royal Dutch Mathematical Society (KWG).Peer reviewe

From Gentzen to Jaskowski and Back : Algorithmic Translation of Derivations Between the Two Main Systems of Natural Deduction

The way from linearly written derivations in natural deduction, introduced by Jaskowski and often used in textbooks, is a straightforward root-first translation. The other direction, instead, is tricky, because of the partially ordered assumption formulas in a tree that can get closed by the end of a derivation. An algorithm is defined that operates alternatively from the leaves and root of a derivation and solves the problem.Peer reviewe

Von Neumann explains his game theory to Gödel, September 1940

Peer reviewe

Can Mathematics be Proved Consistent? : Gödel's Shorthand Notes & Lectures on Incompleteness

Peer reviewe

Kurt Gödel : The Princeton Lectures on Intuitionism

Peer reviewe

Efficacy and safety of epidural, continuous perineural infusion and adjuvant analgesics for acute postoperative pain after major limb amputation - a systematic review

Background and aims: Treatment of pain following major limb amputations is often a clinical challenge in a patient population consisting mainly of elderly with underlying diseases. Literature on management of acute post-amputation pain is scarce. We performed a systematic review on this topic to evaluate the efficacy and safety of analgesic interventions for acute pain following major limb amputation. Methods: A literature search was performed in PubMed, Cochrane Central Register of Controlled Trials and Cochrane Database of Systematic Reviews using the following key words: [(amputation) AND (pain OR analgesi* OR pain relief)] AND (acute OR postoperative). Randomized controlled studies (RCTs) and observational studies investigating treatment of acute pain following major amputations for any indication (peripheral vascular disease, malignant disease, trauma) were included. The review was performed according to the standards described in the PRISMA statement. The Cochrane quality assessment tool was used to evaluate the risk of bias in the RCTs. Results: Nineteen studies with total of 949 patients were included. The studies were generally small and heterogeneous on outcomes, study designs and quality. There were 16 studies on epidural or continuous perineural analgesia CPI). Based on five RCTs (n = 268) and two observational studies (n = 49), epidural analgesia decreased the intensity of acute stump pain as compared to systemic analgesics, during the first 24 h after the operation. Based on one study epidural analgesia caused more adverse effects like sedation, nausea and motor block than continuous perineural local anesthetic infusion. Based on one RCT (n = 21) and eight observational studies (n = 501) CPI seemed to decrease opioid consumption as compared to systemic analgesics only, on the first three postoperative days, and was well tolerated. Only three trials investigated systemic analgesics (oral memantine, oral gabapentine, iv ketamine). Ketamine did not decrease acute pain or opioid consumption after amputation as compared to other systemic analgesics. Gabapentin did not decrease acute pain when combined to epidural analgesia as compared to epidural analgesia and opioid treatment, and caused adverse effects. Conclusions: The main finding of this systematic review is that evidence regarding pain management after major limb amputation is very limited. Epidural analgesia may be effective, but firm evidence is lacking. Epidural causes more adverse effects than CPI. The results on efficacy of CPI are indecisive. The data on adjuvant medications combined to epidural analgesia or CPI is limited. Studies on efficacy and adverse effects of systemic analgesics for amputation pain, especially concentrating on elderly patients, are needed.Peer reviewe

Uutta leikkauksen jälkeisen kivun hoidossa

Väittelijä Hanna von Plato ; Helsingin yliopist

Reformismus oder Sozialfaschismus? Antwort auf Niets Kadritzkes Polemik in PROKLA Nr. 11/12

Der für meine Antwort zur Verfügung gestellte Raum ist klein und meine V orbereitungszeit kurz - deshalb will ich sofort zu:tfl Kem der Auseinandersetzung kommen und nur am Rande auf unwissenschaftliche Fälschungen und die teilweise pfäffische Polemik (1) Kadritzkes eingehen. Der Kern, um den es geht, scheint mir folgender zu sein: Ist die Politik der sozialdemokratischen Führer seit 1914 im Wesen eine Politik des Imperialismus, die große Teile der Arbeiterklasse mithilfe reformistischer Phrasen und in Phasen relativer Stabilität auch mit tatsächlichen Zugeständnissen an den kapitalistischen Staat ketten soll - oder eine Politik des Reformismus, wie Kadritzke meint. Welche Politik betreibt eine sozialdemokratische Parteiführung, wenn das System, mit dem sie auch materiell verwachsen ist, in tiefe ökonomische und politische Krisen gerät und nur noch durch den brutalen Terror über die Arbeiterklasse seine Herrschaft aufrechterhalten kann? Konkret: wie verhielt sich die SPD-Führung zwischen 1928 bis 1933 während der umfassenden Krise und schließlich während des drohenden Faschismus? War der Terrorismus der SPD-Führer nur der widersprüchliche Ausrutscher von Reformisten oder die klare Antwort auf die Alternative: ,,Ja" zum immer terroristischer werdenden Staat oder „Ja" zum Kampf um Reformen, auch mit Kommunisten, um demokratische Rechte und gegen die ökonomische Verelendung im bürgerlichen Staat? Niels Kadritzke bezeichnet die Politik der SPD-Führung in seinem Aufsatz als reformistisch